Question

Factorise x^2 + 1/x^2 - 3

Answer 1

$x^2 + 1/x^2 - 3$

We can Also Write it as

$x^2 + 1/x^2 - 2 \: - 1$

Or also

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

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

We Can Apply 3rd identity here which is

a²-b²=(a-b)(a+b)

$a = x + \frac{1}{x}$

$b = 1$

So,

$(x + \frac{1}{x} + 1)(x + \frac{1}{x} - 1)$