If x⁴ + 1/(x⁴) = 1154, where x > 0, then what is the value of x³ + 1/(x³) ?

If x⁴ + 1/(x⁴) = 1154, where x > 0, then what is the value…

If $x^4 + \frac 1 {x^4} = 1154,$ where x > 0, then what is the value of $x^3 + \frac 1 {x^3}$ ?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 198.

Given that

if $x^4 + \frac 1 {x^4} = 1154,$ x > 0

⇒ (x² + 1/x²)² - 2 = 1154

⇒ (x² + 1/x²)² = 1156

⇒ x² + 1/x² = 34

⇒ (x + 1/x)² - 2 = 34

⇒ x + 1/x = 6

Hence, $x^3 + \frac 1 {x^3}$ = (x + 1/x)³ - 3(x + 1/x) = 6³ - 3 × 6 = 216 - 18 = 198