If x 1 x 6 find x2 1 x2

Asked by admin @ 10/08/2021 in Math viewed by 297 People

If (x-1/x) = 6, then find (x2 + 1/x2) and (x + 1/x)

I found (x2+ 1/x2) = 38
Now how to find (x + 1/x) ?

Answered by admin @ 10/08/2021

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( $(x - \frac{1}{x}) = 6 \\ \\ {(x \ - \frac{1}{x}) }^{2} = {(6) }^{2} \\ \\ ( {x - \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ {(6)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ 36 + 2 = {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ 38 = {x}^{2} + \frac{1}{ {x}^{2} } \: \:$

38 = x^2 +1/x^2

$(x + \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ (x + \frac{1}{x} ) {}^{2} = 38 + 2 \\ \\ (x + \frac{1}{x} ) {}^{2} = 40 \\ \\ (x + \frac{1}{x} ) = \sqrt{40} \\ \\ (x \ + \frac{1}{x} ) = \sqrt{2 \times 2 \times 2 \times 5 } \\ \\ (x + \frac{1}{x} ) = 2 \sqrt{10}$

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If x 1 x 6 find x2 1 x2

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