If x⁴ + 1/(x⁴)= 727, x > 1 , then what is the value of (x-1/x) ?

If x⁴ + 1/(x⁴)= 727, x > 1 , then what is the value of…

If $x^4 + \frac{1}{x^4}= 727, x > 1$ , then what is the value of $(x-\frac{1}{x})$ ?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 5

$x^4 + \frac{1}{x^4}= 727$

By adding 2 on both sides,

⇒ $x^4 + \frac{1}{x^4}+2= 729$

$(x^2+\frac{1}{x^2})^2= 27^2$

$(x^2+\frac{1}{x^2})= 27$

By subtracting 2 from both sides,

$x^2+\frac{1}{x^2}-2= 25$

$(x-\frac{1}{x})^2= 5^2$

$x-\frac{1}{x}=5$