Question

(x^2+1/x^2)-3(x-1/x)-2=0

Answer 1

Step-by-step explanation:

$({x}^{2} + \frac{1}{ {x}^{2} } ) - 3(x - \frac{1}{x} ) - 2 = 0 \\ \\ ({x}^{2} + \frac{1}{ {x}^{2} } - 2) - 3(x - \frac{1}{x} ) = 0 \\ {(x - \frac{1}{x} )}^{2} - 3(x - \frac{1}{x} ) = 0 \\ ((x - \frac{1}{x} )(x - \frac{1}{x} - 3 )) = 0 \\ \\ so \: that \: x - \frac{1}{x} = 0 \: and \: \\ x - \frac{1}{x} - 3 = 0 \\ x - \frac{1}{x} = 3$

Answer 2

Answer:

$({x}^{2} + \frac{1}{ {x}^{2} } ) - 3(x - \frac{1}{x} ) - 2 = 0 \\ \\ ({x}^{2} + \frac{1}{ {x}^{2} } - 2) - 3(x - \frac{1}{x} ) = 0 \\ {(x - \frac{1}{x} )}^{2} - 3(x - \frac{1}{x} ) = 0 \\ ((x - \frac{1}{x} )(x - \frac{1}{x} - 3 )) = 0 \\ \\ so \: that \: x - \frac{1}{x} = 0 \: and \: \\ x - \frac{1}{x} - 3 = 0 \\ x - \frac{1}{x} = 3$