Question

Factorise (x^2 + 1/x^2) -4(x + 1/x) + 6​

Answer 1

Question:

Factorise $\big(x^2 + \frac{1}{x^2}\big) - 4 \big(x + \frac{1}{x}\big) + 6$

Solution:

$\sf \bigg(x^2 + \frac{1}{x^2}\bigg) - 4 \bigg(x + \frac{1}{x}\bigg) + 6 \\\\\sf \mapsto\bigg(x^2 + \frac{1}{x^2}\bigg) + 6- 4 \bigg(x + \frac{1}{x}\bigg) \\ \\ \sf \mapsto\bigg(x^2 + \frac{1}{x^2} + 2 \times \frac{1}{x} \times x \bigg) + 4- 4 \bigg(x + \frac{1}{x}\bigg) \\ \\ \sf \mapsto \bigg(x^2 + \frac{1}{x^2} + 2 \times \frac{1}{x} \times x \bigg) + {2}^{2}- 4 \bigg(x + \frac{1}{x}\bigg) \\ \\ \sf \mapsto \bigg(x + \frac{1}{x} \bigg)^{2} + {2}^{2}- 4 \bigg(x + \frac{1}{x}\bigg) \\ \\ \sf \mapsto\bigg(x + \frac{1}{x } + 2\bigg)\bigg(x + \frac{1}{x } + 2\bigg)- 4 \bigg(x + \frac{1}{x}\bigg)$