Factorise :
x2+1x2−3x^2 + \dfrac{1}{x^2} - 3x2+x21−3
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Given,
=x2+1x2−3=x2+1x2−2−1=(x−1x)2−12=(x−1x+1)(x−1x−1).\phantom{=}x^2 + \dfrac{1}{x^2} - 3 \\[1em] = x^2 + \dfrac{1}{x^2} - 2 - 1 \\[1em] = \Big(x - \dfrac{1}{x}\Big)^2 - 1^2 \\[1em] = \Big(x - \dfrac{1}{x} + 1\Big)\Big(x - \dfrac{1}{x} - 1\Big).=x2+x21−3=x2+x21−2−1=(x−x1)2−12=(x−x1+1)(x−x1−1).
Hence, x2+1x2−3=(x−1x+1)(x−1x−1).x^2 + \dfrac{1}{x^2} - 3 = \Big(x - \dfrac{1}{x} + 1\Big)\Big(x - \dfrac{1}{x} - 1\Big).x2+x21−3=(x−x1+1)(x−x1−1).
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