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If sqrt x + frac 1 sqrt x = 3 &nbsp...

This question belongs to Arithmetic Ability Algebra
Algebra
?

If $$\sqrt x + \frac{1}{{\sqrt x }} = 3,$$   then the value of $${x^3} + \frac{1}{{{x^3}}}$$  is:

Answer & Solution
Correct Answer: Option B
$$\eqalign{ & \sqrt x + \frac{1}{{\sqrt x }} = 3 \cr & x + \frac{1}{x} = 7 \cr & {x^3} + \frac{1}{{{x^3}}} = {7^3} - 3 \times 7 \cr & = 343 - 21 \cr & = 322 \cr} $$
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