{"id":3629,"date":"2021-01-30T12:15:29","date_gmt":"2021-01-30T12:15:29","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3629"},"modified":"2022-03-23T19:32:15","modified_gmt":"2022-03-23T19:32:15","slug":"%e0%a6%85%e0%a6%aa%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%b8%e0%a6%99%e0%a7%8d%e0%a6%97%e0%a6%bf%e0%a6%95-%e0%a6%ae%e0%a7%82%e0%a6%b2","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/%e0%a6%85%e0%a6%aa%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%b8%e0%a6%99%e0%a7%8d%e0%a6%97%e0%a6%bf%e0%a6%95-%e0%a6%ae%e0%a7%82%e0%a6%b2\/","title":{"rendered":"\u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 (Extraneous Root)"},"content":{"rendered":"

\u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 (<\/b>Extraneous Root):<\/b><\/h2>\n

\u09af\u09c7 \u09b8\u09ae\u09b8\u09cd\u09a4 \u09ae\u09c2\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09b8\u09bf\u09a6\u09cd\u09a7 \u0995\u09b0\u09c7 \u09a8\u09be \u09a4\u09be\u09a6\u09c7\u09b0\u0995\u09c7 \u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u09af\u09a6\u09bf \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09ac\u09b0\u09cd\u0997 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u098f\u0995 \u09ac\u09be \u098f\u0995\u09be\u09a7\u09bf\u0995 \u09ae\u09c2\u09b2 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09af\u09be\u09a6\u09c7\u09b0 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09b8\u09bf\u09a6\u09cd\u09a7 \u09b9\u09af\u09bc \u09a8\u09be\u0964<\/span><\/p>\n

\u09af\u09c7\u09ae\u09a8:<\/b> <\/b>cosx <\/span>– sinx <\/span> = 1<\/strong> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09a8\u09bf\u09ae\u09cd\u09a8\u09c7\u09b0 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09a4\u09c7 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09c7 \u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc:<\/b>\u00a0<\/b><\/p>\n

cosx <\/span>– sinx <\/span>=1 \u21d2cosx <\/span>=1+ sinx <\/span><\/span>\u00a0<\/span><\/p>\n

\u21d2\\cos ^{2} x <\/span>=1+\\sin x <\/span>+ \\sin ^{2} x<\/span><\/span>\u00a0<\/span><\/p>\n

\u21d21-\\sin ^{2} x <\/span><\/span>=1+ \\sin x<\/span>+\\sin ^{2} x <\/span><\/span>\u00a0<\/span><\/p>\n

\u21d22\\sin ^{2} x <\/span><\/span>+2 \\sin x <\/span>=0<\/span>\u00a0<\/span><\/p>\n

\u21d2 \\sin x <\/span>( \\sin x <\/span>+ 1 )=0<\/span>\u00a0<\/span><\/p>\n

\u09af\u09a6\u09bf<\/span> \\sin x <\/span><\/span>=0<\/span> \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 <\/span>x <\/span>=n \\pi <\/span>,n <\/span>\u2208\\mathbb{Z} <\/span><\/span><\/p>\n

\u09af\u09a6\u09bf<\/span> \\sin x <\/span><\/span>+1=0\u21d2 \\sin x <\/span>=-1<\/span> \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7<\/span> x <\/span>=(4n <\/span>-1)<\/span>2<\/span>, n <\/span>\u2208\\mathbb{Z} <\/span><\/span><\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 x <\/span><\/span>=\u00b1 \\pi\u00a0<\/span><\/span>\u00b1 3\\pi <\/span><\/span>\u00b1 5\\pi <\/span><\/span>,\u2026\u2026<\/span> \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09ae\u09c2\u09b2 \\cos x <\/span>– \\sin x <\/span><\/span>=1<\/span>\u00a0<\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09b8\u09bf\u09a6\u09cd\u09a7 \u0995\u09b0\u09c7\u09a8\u09be\u0964<\/span><\/p>\n

\u09a4\u09be\u0987 \u098f\u0996\u09be\u09a8\u09c7 x <\/span><\/span>=\u00b1 \\pi\u00a0<\/span>\u00b1 3\\pi <\/span>\u00b1 5\\pi <\/span>,\u2026\u2026 \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09ae\u09c2\u09b2 \\cos x <\/span>– \\sin x <\/span><\/span>,\u2026\u2026<\/span> \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 \u098f\u09ac\u0982<\/span> \\cos x <\/span><\/span>– \\sin x <\/span>=1<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u09b9\u09ac\u09c7, x <\/span><\/span>=2n \\pi<\/span>,(4n <\/span>-1)2<\/span>,\u00a0<\/span>\u09af\u09c7\u0996\u09be\u09a8\u09c7 n <\/span>\u2208\\mathbb{Z} <\/span><\/span><\/p>\n

\u098f\u0987 \u099c\u09be\u09a4\u09c0\u09af\u09bc<\/span>\u00a0<\/span>( acosx<\/span>+bsinx <\/span>=c <\/span>)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7 \u09af\u09be\u09a4\u09c7 \u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u09a8\u09be \u0998\u099f\u09c7 \u098f\u099c\u09a8\u09cd\u09af \u09a8\u09bf\u09ae\u09cd\u09a8\u09c7\u09b0 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc: \\cos x <\/span>– \\sin x <\/span><\/span>=1<\/span><\/p>\n

\\frac{1}{\\sqrt{2}} <\/span><\/span>cosx <\/span>– \\cos x-\\frac{1}{\\sqrt{2}}<\/span><\/span>sinx <\/span>=\\frac{1}{\\sqrt{2}} <\/span><\/span>[\u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \\sqrt{1^{2}+1^{2}}= <\/span>\\sqrt{2} <\/span><\/span>\u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ad\u09be\u0997 \u0995\u09b0\u09c7]<\/span><\/p>\n

\u21d2 \\cos x <\/span>.\\cos \\frac{\\pi}{4} <\/span><\/span>– \\sin x <\/span>. \\sin \\frac{\\pi}{4}<\/span><\/span>=\\cos \\frac{\\pi}{4} <\/span><\/span><\/p>\n

\u21d2\\cos \\left(x+\\frac{\\pi}{4}\\right) <\/span><\/span>=\\cos \\frac{\\pi}{4} <\/span><\/span>\u00a0<\/span><\/p>\n

\u2234x <\/span>+\\frac{\\pi}{4} <\/span><\/span>=2n \\pi<\/span> \\pm\\frac{\\pi}{4}<\/span>\u09af\u09c7\u0996\u09be\u09a8\u09c7 n <\/span>\u2208\\mathbb{Z} <\/span><\/span><\/p>\n

\u21d2x <\/span>+\\frac{\\pi}{4} <\/span>=2n \\pi<\/span> +\\frac{\\pi}{4}<\/span><\/span>\u21d2 x<\/span>=2n \\pi<\/span><\/span>\u00a0<\/span><\/p>\n

\u0985\u09a5\u09ac\u09be, x <\/span>+\\frac{\\pi}{4} <\/span><\/span>=2n \\pi<\/span> – \\frac{\\pi}{4}<\/span><\/span>\u21d2x <\/span>=2n \\pi<\/span>-2\\frac{\\pi}{4} <\/span><\/span><\/p>\n

\u21d2x <\/span>=2\\frac{\\pi}{4} <\/span>–\\frac{\\pi}{2} <\/span><\/span>\u00a0<\/span><\/p>\n

\u2234x <\/span>=(4n <\/span>-1)\\frac{\\pi}{2} <\/span>\u00a0<\/span>\u00a0<\/span><\/p>\n

\u2234<\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09b8\u09ae\u09be\u09a7\u09be\u09a8x <\/span>=(4n <\/span>-1)\\frac{\\pi}{2} <\/span>\u00a0\u00a0<\/span>,\u00a0<\/span>\u09af\u09c7\u0996\u09be\u09a8\u09c7 n <\/span>\u2208\\mathbb{Z} <\/span><\/span><\/p>\n

\u09a6\u09c3\u09b7\u09cd\u099f\u09bf \u0986\u0995\u09b0\u09cd\u09b7\u09a3 <\/b>(Attention):<\/b><\/h3>\n

\u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7 \u09b8\u09c0\u09ae\u09be \u0985\u09b0\u09cd\u09a5\u09be\u09ce<\/span>\u00a0<\/span>–\\pi <\/span><\\theta <\/span><\\pi <\/span><\/span> \u09ac\u09be, –2\\pi <\/span><\\theta <\/span><2\\pi <\/span><\/span> \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09a5\u09be\u0995\u09b2\u09c7, \u0986\u09ae\u09b0\u09be \u09b8\u09c1\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u03b8<\/span><\/span><\/span><\/span><\/span> <\/span> \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09bf\u0964 <\/span>n <\/span> \u098f\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09ae\u09be\u09a8\u0997\u09c1\u09b2\u09cb\u09b0 \u09af\u09c7\u0997\u09c1\u09b2\u09cb \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09be\u099d\u09c7 \u09a5\u09be\u0995\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u0997\u09cd\u09b0\u09b9\u09a3 \u0995\u09b0\u09c7, \u09ac\u09be\u0995\u09bf\u0997\u09c1\u09b2\u09cb \u09ac\u09be\u09a6 \u09a6\u09c7\u0987\u0964 \u098f\u0987 process \u0985\u09a8\u09c7\u0995 \u09b8\u09ae\u09af\u09bc consume \u0995\u09b0\u09c7\u0964 \u09ac\u09bf\u09b6\u09cd\u09ac\u09be\u09b8 \u09a8\u09be \u09b9\u09b2\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u0985\u0982\u0995\u099f\u09bf Solve \u0995\u09b0\u09c7 \u09a6\u09c7\u0996\u0964 \u0986\u09ae\u09b0\u09be \u098f\u0995\u099f\u09c1 \u0985\u09a8\u09cd\u09af process \u098f Solve \u0995\u09b0\u09ac, \u09af\u09c7\u0996\u09be\u09a8\u09c7 n <\/span><\/span>\u00a0\u098f\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09ae\u09be\u09a8\u0997\u09c1\u09b2\u09cb \u0986\u0997\u09c7\u0987 \u099c\u09be\u09a8\u09be \u09af\u09be\u09ac\u09c7\u0964 \u09a4\u09be\u09b0\u09aa\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7<\/span> n <\/span><\/span>\u00a0\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u03b8<\/span><\/span><\/span><\/span><\/span><\/span> \u098f\u09b0 \u09af\u09a5\u09be\u09b0\u09cd\u09a5 \u09ae\u09be\u09a8 \u09ac\u09c7\u09b0 \u0995\u09b0\u09ac\u0964 \u09a8\u09bf\u099a\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09a6\u09c7\u0996\u09be \u09af\u09be\u0995-<\/span><\/p>\n

2\\sin ^{2} x <\/span><\/span>+ \\sin ^{2} 2 x<\/span><\/span>=2,\u00a0 \u00a0 [ –2\\pi <\/span><\\theta <\/span><2\\pi <\/span> ]<\/span><\/p>\n

\u21d21-\\cos 2 x <\/span>+1- \\cos ^{2} 2 x<\/span><\/span>=2<\/span>\u00a0<\/span><\/p>\n

\u21d2-\\cos 2 x <\/span>(\\cos 2 x <\/span>+1)=0<\/span>\u00a0<\/span><\/p>\n

\u2234\\cos 2 x <\/span>=0\u21d2<\/span>2x <\/span>= (2n+1)<\/span> \\frac{\\pi}{2}<\/span>\u21d2x <\/span><\/span>\u00a0= (2n+1)<\/span> \\frac{\\pi}{4}<\/span><\/span><\/p>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1, –2\\pi <\/span><\\theta <\/span><2\\pi <\/span>\u21d2-2\\pi <\/span><\/span>< \\frac{\\pi}{4}<\/span><\/span><2\\pi <\/span><\/span>\u00a0<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, <\/span> cos2x<\/span>+1=0<\/span><\/p>\n

\u21d2\\cos 2 x <\/span>=-1\u21d2 2x<\/span>=(2n <\/span>+1) \\pi<\/span><\/p>\n

\u21d2x <\/span>= (2n+1)<\/span> \\frac{\\pi}{2}<\/span><\/span><\/p>\n

\u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u0993 – 2 \\pi<\/span><(2n <\/span>+1) \\frac{\\pi}{2}<\/span><\/span>< 2 \\pi<\/span><\/span>\u21d2-<\/span>5<2n <\/span><3<\/span><\/p>\n

n <\/span>=-2, -1, 0, 1,<\/span> \u2234x <\/span>=-3. \\frac{\\pi}{2}<\/span><\/span>, – \\frac{\\pi}{2}<\/span><\/span>, \\frac{\\pi}{2}<\/span><\/span>, 3 \\frac{\\pi}{2}<\/span><\/span><\/p>\n

\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09af\u09bc \u09b8\u09ae\u09be\u09a7\u09be\u09a8: <\/span>x=-7 \\frac{\\pi}{4}<\/span><\/span>, -5 \\frac{\\pi}{4}<\/span><\/span>, -3 \\frac{\\pi}{4}<\/span><\/span>, – \\frac{\\pi}{4}<\/span><\/span>, \\frac{\\pi}{4}<\/span><\/span>, 3. \\frac{\\pi}{4}<\/span><\/span>, 5. \\frac{\\pi}{4}<\/span><\/span>, 7. \\frac{\\pi}{4}<\/span><\/span>,-3. \\frac{\\pi}{2}<\/span><\/span>, – \\frac{\\pi}{2}<\/span><\/span>, \\frac{\\pi}{2}<\/span><\/span>,\u00a0<\/span>3 \\frac{\\pi}{2}<\/span><\/span>\u00a0<\/span>\u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/span>\u00a0<\/span>12<\/span> \u099f\u09bf\u00a0<\/span><\/p>\n

\u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u099f\u09bf \u09ac\u09c7\u09b6 \u09ac\u09a1\u09bc \u09ae\u09a8\u09c7 \u09b9\u099a\u09cd\u099b\u09c7, \u09a4\u09be\u0987 \u09a8\u09be\u0964 \u0986\u09b8\u09b2\u09c7 practice \u0995\u09b0, \u0986\u09b0\u0993 \u099b\u09cb\u099f \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09aa\u09c1\u09b0\u09a8\u09cb \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09a4\u09c7 \u0995\u09b0\u09c7 \u09a6\u09c7\u0996 \u0995\u09a4 \u09ac\u09a1\u09bc \u09b9\u09af\u09bc, \u0986\u09b0<\/span>\u00a0<\/span>12<\/span> \u099f\u09bf \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u0995\u09bf\u09a8\u09be?<\/span><\/p>\n

\u21d28<2n <\/span>+1<8\u21d2-9<2n <\/span><7\u2026\u2026(i)<\/span>\u00a0<\/span><\/p>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1, n <\/span>\u2208\\mathbb{Z} <\/span><\/span>\u00a0\u09a4\u09be\u0987 \u09a6\u09c7\u0996\u09bf, n <\/span><\/span>\u00a0\u098f\u09b0 \u0995\u09cb\u09a8 \u09ae\u09be\u09a8\u0997\u09c1\u09b2\u09cb\u09b0 \u099c\u09a8\u09cd\u09af (i) \u09a8\u0982 \u0985\u09b8\u09ae\u09a4\u09be\u099f\u09bf \u09b8\u09bf\u09a6\u09cd\u09a7,<\/span> n <\/span>\u00a0<\/span>=-4,\u00a0-3,\u00a0-2,\u00a0-1,\u00a00,\u00a01,\u00a02,\u00a03<\/span><\/p>\n

\u098f\u0987 \u09ae\u09be\u09a8\u0997\u09c1\u09b2\u09cb \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987, x <\/span>\u00a0<\/span>=-7 \\frac{\\pi}{4}<\/span><\/span>, -5 \\frac{\\pi}{4}<\/span><\/span>, -3 \\frac{\\pi}{4}<\/span><\/span>,\u00a0–<\/span>4<\/span>, \\frac{\\pi}{4}<\/span><\/span>, 3. \\frac{\\pi}{4}<\/span><\/span>, 5. \\frac{\\pi}{4}<\/span><\/span>, 7. \\frac{\\pi}{4}<\/span><\/span><\/p>\n

\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09cd\u09af\u09ac\u09a7\u09bf\u09a4\u09c7 \u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 <\/b>(<\/b>Solution of trigonometric equation in a finite interval)<\/b><\/h3>\n

\u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u0995 \u09ab\u09be\u0982\u09b6\u09a8 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u09ac\u09c3\u09a4\u09cd\u09a4 \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u098f\u09b0 \u09ae\u09be\u09a8\u0997\u09c1\u09b2\u09cb \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09cd\u09b0\u09ae\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09cd\u09af\u09ac\u09a7\u09bf\u09a4\u09c7\u0993 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7\u09b0 \u09aa\u09c1\u09a8\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09bf \u09b9\u09af\u09bc\u0964 \u09a4\u09cd\u09b0\u09bf\u0995\u09cb\u09a3\u09ae\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u09a5\u09c7\u0995\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09cd\u09af\u09ac\u09a7\u09bf\u09a4\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09ae\u09be\u09a8\u0997\u09c1\u09b2\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u0986\u09ac\u09be\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09cd\u09af\u09ac\u09a7\u09bf\u09a4\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0997\u09c1\u09b2\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\u09a8\u09bf\u09ae\u09cd\u09a8\u09c7 \u09b2\u09c7\u0996\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7\u09b0 \u0995\u09cc\u09b6\u09b2 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09be \u09b9\u09b2\u09cb:<\/strong><\/p>\n

(i) \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09ac\u09cd\u09af\u09ac\u09a7\u09bf\u09a4\u09c7 \u09ab\u09be\u0982\u09b6\u09a8\u09c7\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u0985\u0999\u09cd\u0995\u09a8 (\u09ae\u09c1\u0995\u09cd\u09a4 \u09b9\u09b8\u09cd\u09a4\u09c7) \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

(ii) \u09ab\u09be\u0982\u09b6\u09a8\u09c7\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6\u09bf\u09a4 \u09b8\u09cd\u09a5\u09be\u09a8\u09c7 x <\/span><\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b0\u09c7\u0996\u09be \u0986\u0981\u0995\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

(iii) \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u09b0\u09c7\u0996\u09be\u099f\u09bf \u09ab\u09be\u0982\u09b6\u09a8\u0995\u09c7 \u09af\u09a4\u09ac\u09be\u09b0 \u099b\u09c7\u09a6 \u0995\u09b0\u09ac\u09c7 \u09a0\u09bf\u0995 \u09a4\u09a4\u099f\u09bf \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8 \u09a5\u09be\u0995\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

(iv) \u099b\u09c7\u09a6\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09c1\u09b2\u09bf\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae\u09a4\u09be \u09ac\u09be \u09ab\u09be\u0982\u09b6\u09a8\u09c7\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09be\u09b2 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u0985\u09a4\u0983\u09aa\u09b0 \u099b\u09c7\u09a6\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09c1\u09b2\u09bf\u09b0 <\/span>x<\/span> \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995\u0987 \u09ab\u09be\u0982\u09b6\u09a8\u09c7\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 (Extraneous Root): \u09af\u09c7 \u09b8\u09ae\u09b8\u09cd\u09a4 \u09ae\u09c2\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09b8\u09bf\u09a6\u09cd\u09a7 \u0995\u09b0\u09c7 \u09a8\u09be \u09a4\u09be\u09a6\u09c7\u09b0\u0995\u09c7 \u0985\u09aa\u09cd\u09b0\u09be\u09b8\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09c2\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u09af\u09a6\u09bf \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09ac\u09b0\u09cd\u0997 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u098f\u0995 \u09ac\u09be \u098f\u0995\u09be\u09a7\u09bf\u0995 \u09ae\u09c2\u09b2 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09af\u09be\u09a6\u09c7\u09b0 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09b8\u09bf\u09a6\u09cd\u09a7 \u09b9\u09af\u09bc<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3026,4272,3038,50],"tags":[2573,2571,1592,2574,2572],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3629"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3629"}],"version-history":[{"count":13,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3629\/revisions"}],"predecessor-version":[{"id":7921,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3629\/revisions\/7921"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3629"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}