Question

Factorise x ^ 4 + 1/x ^ 4 - 3​

Answer 1

Answer:

Step-by-step explanation:

Add 1 and subtract 1, so that the expression won't change.

$x^{4}+\frac{1}{x^{4}}-3=x^{4}+\frac{1}{x^{4}}-3 +1 - 1\\\\=x^{4}+\frac{1}{x^{4}} - 2 + 1\\\\= (x^{2})^{2} + (\frac{1}{x^{2}})^{2}- 2 *x^{2}*\frac{1}{x^{2}} - 1$

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

(a² - b²) = (a+b)(a - b)

Here a = x² - (1/x²)  and b = 1

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