Question

If x2 +1/x2 =23 find the value of x-1/x

Answer 1

${(x - \frac{1}{x} )}^{2} = {x}^{2} + { (\frac{1}{x}) }^{2} - 2 \\ x - \frac{1}{x} = \sqrt{{x}^{2} + { (\frac{1}{x}) }^{2} - 2} \\ x - \frac{1}{x} = \sqrt{23 - 2} \\ x - \frac{1}{x} = \sqrt{21} \\ x - \frac{1}{x} = \sqrt {21}\: or \: - \sqrt {21}$

hope it helps

Answer 2

Heya

______________________________

Let

x - 1/x = y

SQUARING BOTH SIDE'S

( x -1/x )² = y²

=>

x² + 1/x² - 2 = y²

=>

y² = 23 - 2

=>

y² = 21

=>

y = +√21

OR

y = -√21

=>

(x - 1/x) = √21

OR

(x - 1/x) = -√21