Question

If \({x^4} + \frac{1}{{{x^4}}} = 47\), then find \(x + \frac{1}{x}\)

1. 9
2. 5
3. 3
4. 7

Answer 1

Correct Answer - Option 3 : 3

As we know,

(a + b)² = a² + 2ab + b²

(x² + 1/x²)² = x⁴ + 1/x⁴ + 2

⇒ (x² + 1/x²)² = 47 + 2 = 49

⇒ (x² + 1/x²) = √49

⇒ x² + 1/x² = 7

Now,

(x + 1/x)² = x² + 1/x² + 2

⇒ (x + 1/x)² = 7 + 2

⇒ (x + 1/x) = √9

∴ x + 1/x = 3