If x⁴+1/(x⁴)=47 , then what is the value of x³+1/(x³)?

If $x^4+\frac{1}{x^4}=47$ , then what is the value of $x^3+\frac{1}{x^3}?$

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 18.

$x^4+\frac{1}{x^4}=47$

⇒ $x^2+\frac{1}{x^2}$ = √(47 + 2) = √49 = 7

⇒ $x+\frac{1}{x}$ = √(7 + 2) = √9 = 3

⇒ $x^3+\frac{1}{x^3}$ = 3³ - 3 × 3 = 27 - 9 = 18

SSC CHSL 2023 PYQ — Question 56