Question

Factorise : $x^2-2+\frac{1}{x^2}-y^2$

Answer 1

Given : $x^2-2+\frac{1}{x^2}-y^2$

We can further write it as

$x^2-2+\frac{1}{x^2}-y^2$$=(x^2-2\times x^2\times \frac{1}{x^2}+\frac{1}{x^2})-y^2$

So we get

$x^2-2+\frac{1}{x^2}-y^2$$={(x-\frac{1}{x})}^2-y^2$

Based on the equation $a^2-b^2=(a+b)(a-b)$

We get,

$x^2-2+\frac{1}{x^2}-y^2$$=(x-\frac{1}{x}+y)(x-\frac{1}{x}-y)$