Question

If x
$x {}^{2} + \frac{1}{x {}^{2} } = 27 \: find \: the \: value \: of \: x - \frac{1}{x}$
​

Answer 1

Solution:

• x² + 1/x² = 27

Note:

=> x(1/x) = 1

» x² + 1/x² = 27

Subtract 2 on both sides

» x² - 2(1)(1/x) + 1/x² = 25

» (x - 1/x)² = 25

On taking square root

» x - 1/x = 5

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 25 \\ ( {x - \frac{1}{x} })^{2} = 25 \\ x - \frac{1}{x} =± 5$