CUET Preparation Today
CUET
General Aptitude Test
Quantitative Reasoning
Algebra
If \(\sqrt {x}\) + \(\frac{1}{\sqrt {x}}\) = \(\sqrt {6}\)
Find x6 + \(\frac{1}{x^6}\).
2702
5404
1351
1021
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
