Solution
$$\sqrt x - \frac{1}{\sqrt x} = 4$$
Squaring both side,
$$\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^2=4^2$$
$$x+\frac{1}{x}=16+2=18$$
Again squaring both side we get,
$$\left(x+\frac{1}{x}\right)^2=18^2$$
$$x^2+\frac{1}{x^2}+2=324$$
$$x^2+\frac{1}{x^2}=322$$
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