General Aptitude TestQuantitative ReasoningAlgebra

If sqrt x + frac1sqrt x = sqrt 6 Find x6 + 1/(x^6) .

If \(\sqrt {x}\) + \(\frac{1}{\sqrt {x}}\) = \(\sqrt {6}\)

Find x⁶ + \(\frac{1}{x^6}\).

Answer & explanation

Correct answer: option 1

The correct answer is Option 1: 2702

a³ + b³ = (a + b)³ − 3ab(a + b)

Here,
a = x² and b = 1/x²

So,
ab = x² × (1/x²) = 1

Also,
a + b = x² + 1/x² = 14

Therefore,

x⁶ + 1/x⁶
= (x² + 1/x²)³ − 3(x² × 1/x²)(x² + 1/x²)
= 14³ − 3(1)(14)
= 2744 − 42
= 2702