Question

find the factor of above equation​

Answer 1

Answer:

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

Using this in question,

$(x - \frac{1}{x} ) {}^{2} + 2 + 2(x - \frac{1}{x}) - 5 =$

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

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

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

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

$(x - \frac{1}{x} + 3)(x - \frac{1}{x} - 1)$

so option C is correct.