Factorise :
x2+1x2−11x^2 + \dfrac{1}{x^2} - 11x2+x21−11
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Given,
=x2+1x2−11=x2+1x2−2−9=(x−1x)2−9=(x−1x)2−32=(x−1x+3)(x−1x−3).\phantom{=} x^2 + \dfrac{1}{x^2} - 11 \\[1em] = x^2 + \dfrac{1}{x^2} - 2 - 9 \\[1em] = \Big(x - \dfrac{1}{x}\Big)^2 - 9 \\[1em] = \Big(x - \dfrac{1}{x}\Big)^2 - 3^2 \\[1em] = \Big(x - \dfrac{1}{x} + 3\Big)\Big(x - \dfrac{1}{x} - 3\Big).=x2+x21−11=x2+x21−2−9=(x−x1)2−9=(x−x1)2−32=(x−x1+3)(x−x1−3).
Hence, x2+1x2−11=(x−1x+3)(x−1x−3).x^2 + \dfrac{1}{x^2} - 11 = \Big(x - \dfrac{1}{x} + 3\Big)\Big(x - \dfrac{1}{x} - 3\Big).x2+x21−11=(x−x1+3)(x−x1−3).
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