If x⁴ + x⁻⁴ = 47, x > 0, then what is the value of x + 1/x - 2 ?

If x⁴ + x⁻⁴ = 47, x > 0, then what is the value of x + 1/x…

If x⁴ + x^-4 = 47, x > 0, then what is the value of $x + \frac 1 x - 2$ ?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 1.

Given that

If x⁴ + x^-4 = 47, x > 0,

Calculation

⇒ x⁴ + x^-4 + 2 = 47 + 2 = 49

⇒ (x² + x^-2)² = 49

⇒ x² + 1/x² = 7

By adding 2 on both sides

⇒ x² + 1/x² + 2 = 7 + 2 = 9

⇒ (x + 1/x)² = 9

⇒ x + 1/x = 3

Hence, $x + \frac 1 x - 2$ = 3 - 2 = 1