If x⁴ + 1 over x⁴ = 2, and x is a positive quantity, then x is equal to:

If x⁴ + 1 over x⁴ = 2, and x is a positive quantity, then…

If x⁴ + ${1 \over x^4}$ = 2, and x is a positive quantity, then x is equal to:

Show answer & explanation

Correct answer: A

Explanation

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

Given, x⁴ + ${1 \over x^4}$ = 2

⇒ $x^4 + \frac{1}{x^4} + 2 = 4$

⇒ $x^2 + \frac{1}{x^2} = 2$

Also, $x^2 + \frac{1}{x^2} + 2 = 4$

⇒ $x + \frac{1}{x} = 2$

⇒ x² - 2x + 1 = 0

⇒ (x - 1)(x - 1) = 0

⇒ x = 1