Question

find the value of x²+1/x²
when x+1/x=3 and x+1/x=11
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Answer 1

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Answer 2

Step-by-step explanation:

I) Given that,

$x + \frac{1}{x} = 3$

Squaring on both sides, we get,

${(x + \frac{1}{x} )}^{2} = {3}^{2} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 = 7$

II) Given that,

$x + \frac{1}{x} = 11$

Squaring on both sides, we get,

${(x + \frac{1}{x} )}^{2} = {11}^{2} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 121 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 121 - 2 = 119$

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