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Question

If $x^{2} + \frac{1}{x^{2}} = 51$ , find $x - \frac{1}{x}$ .
$4$
$5$
$6$
$7$

A

4

B

5

C

6

D

7

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Solution

Verified by Toppr

$x^{2} + \frac{1}{x^{2}} = 51$

$x - \frac{1}{x} = ?$

Apply the formula $(a - b)^{2} = a^{2} + b^{2} - 2 a b$

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

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

$= 51 - 2 = 49$

$x - \frac{1}{x} = \sqrt{49} = 7$

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