Question

If
$x + \frac{1}{x} = 5$
Find
${x}^{2} + \frac{1}{ {x}^{2} }$
​

Answer 1

$\: \: \: \: \: \: \: \: \: x + \frac{1}{x} = 5 \\ \\ = = > {(x + \frac{1}{x}) }^{2} = {(5)}^{2} \\ \\ = = > {x}^{2} + \frac{1}{ {x}^{2} } + 2.x. \frac{1}{x} = 25 \\ \\ = = > {x}^{2} + \frac{1}{ {x}^{2} } = 25 - 5 \\ \\ = = > {x}^{2} + \frac{1}{ {x}^{2} } = 23$

Answer 2

Answer:

x + 1/x = 5

(x + 1/x)² = (5)²

x² +1/x² +2 = 25

x² + 1/x² = 25-2

x² + 1/x²= 23 ans.

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