Question 67

If $$\sqrt{x} - \frac{1}{\sqrt{x}} = \sqrt{5}$$, then $$x^2 + \frac{1}{x^2}$$ is equal to:

Solution

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

Squaring both the sides , we get,

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

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

Squaring again ,

$$x^2 + \frac{1}{x^2} + 2 =49$$

$$x^2 + \frac{1}{x^2}$$ = 47

So , the answer would be option c)47.

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