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Expansion of (x-y)^2

If x-1x=1 t...

Question

If $x - \frac{1}{x} = 1$ then what is the value of $x^{2} + \frac{1}{x^{2}}$ ?

A

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B

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C

2

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D

3

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Solution

The correct option is A $3$
$[x - (\frac{1}{x})] = 1 (x - (\frac{1}{x}))^{2} = 1^{2} x^{2} + (\frac{1}{x})^{2} - 2 = 1 x^{2} + (\frac{1}{x})^{2} = 3$

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