Question

if x +1/x=4,then find the value of x^2+1/x^2

Answer 1

Identity used :

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$


Given,
$x + \frac{1}{x} = 4$

Squaring both the sides we get,

${(x + \frac{1}{x} )}^{2} = {(4)}^{2} \\ \\ {(x)}^{2} + {( \frac{1}{x}) }^{2} + 2 \times x \times \frac{1}{x} = 16 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14$

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