Question 59

If $$\sqrt x + \frac{1}{\sqrt x} = \sqrt7, then x^3 + \frac{1}{x^3}$$ is equal to:

Solution

$$(\sqrt x + \frac{1}{\sqrt x}) ^ 2$$ = x + $$\frac{1}{x}$$ + 2 = 7

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

$$( x + \frac{1}{ x}) ^ 3$$ = $$x^3 + \frac{1}{ x}^3$$ + 3 * x * $$\frac{1}{x}$$ (x + $$\frac{1}{x}$$)

125 = $$x^3 + \frac{1}{x^3}$$ + 15

$$x^3 + \frac{1}{x^3}$$ =110

So , the answer would be option a)110.

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