Question

Ifx-1/x=√5 find the value of x^2+1/x^2

Answer 1

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Answer 2

Answer:

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$x-\frac{1}{x}=\sqrt{5}$

Squaring on both sides

$(x-\frac{1}{x}) ^{2} =5$

The equation becomes

$x^{2}-2*x*\frac{1}{x} +\frac{1}{x^{2}} =5$

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

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

Hence , answer is

$x^{2}+\frac{1}{x^{2}} =7$