Question

if x+ 1/x=2,find the value of x²+ 1/x²

$x + \frac{1}{x} = 2...value \: of \: {x}^{2} + 1 \div {x}^{2}$

Answer 1

$x + \frac{1}{x} = 2 \\ \\ square \: both \: sides: \\ \\ {(x + \frac{1}{x} )}^{2} = {2}^{2} \\ \\ {x}^{2} + 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 4 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 4 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 4 - 2 \\ \\ \boxed{{x}^{2} + \frac{1}{ {x}^{2} } = 2}$

Answer 2

heya Mate here is your answer

$<u>$

given
$x + \frac{1}{x} = 2 \\ squaring \: both \: sides \: \\ \\ ({x + \frac{1}{x}) }^{2} = {2}^{2}$

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


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

hence the required answer is 2

hope it helps you

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