Question

if x² +1/x²=17, find x - 1/x​

Answer 1

ANSWER:

√(15)

EXPLANATION:

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

SUBTRACT BY 2 ON BOTH SIDES.

${x}^{2} + \frac{1}{ {x}^{2} } - 2 = 17 - 2 \\ {(x - \frac{1}{x}) }^{2} = 15 \\ take \: square \: root \: on \: both \: sides \\ x - \frac{1}{x} = \sqrt{15}$