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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