Question

if x+1/x=2½ find the value of x2+1/x2​

Answer 1

$\huge \bf \underline{ \underline{Solution}}$

$= x + \frac{1}{x} = 2 \frac{1}{2} \\ = x + \frac{1}{x} = \frac{5}{2}$

Squaring both sides,

$=( x + \frac{1}{x} )^{2} = \frac{25}{4}$

$= {x}^{2} + \frac{1}{ {x}^{2} } + 2x \times \frac{1}{x} = \frac{25}{4} \\ = {x}^{2} + \frac{1}{ {x}^{2} } + 2 = \frac{25}{4} \\ = {x}^{2} + \frac{1}{ {x}^{2} } = \frac{25}{4} - 2 \\ = {x}^{2} + \frac{1}{ {x}^{2} } = \frac{25 - 8}{4}$

$= {x}^{2} + \frac{1}{ {x}^{2} } = \frac{13}{4}$

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Final Answer:-

$\mathtt {{x}^{2} + \frac{1}{ {x}^{2} } = \frac{13}{4}}$

Answer 2

$\huge\red{\underline{\overline{\tt\:Answer}}\mid}$

$\huge \frac{13}{4}$

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