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Finding Square of a Number Using Identity

Solve for x: ...

Question

Solve for x:
$\sqrt{x + \frac{1}{x}} = 0$

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Solution

Given that,

$\sqrt{x + \frac{1}{x}} = 0$

$\sqrt{\frac{x^{2} + 1}{x}} = 0$

$\sqrt{x^{2} + 1} = 0$

$x^{2} + 1 = 0$

$x = \sqrt{- 1}$

$x = i$

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