For x > 0 with x⁴ + 1/x⁴ = 47, what is x³ + 1/x³?

18. x² + 1/x² = √(47 + 2) = 7, then x + 1/x = √(7 + 2) = 3, so x³ + 1/x³ = 27 − 9 = 18.

For $x$ > 0 with $x^{4} + 1/ x^{4} = 47$ , what is $x^{3} + 1/ x^{3}$ ?

Competition practiceAlgebra

x^{2} + 1/ x^{2}

= √

(47 + 2) = 7

, then

x + 1/ x

= √

(7 + 2) = 3

, so

x^{3} + 1/ x^{3} = 27 - 9 = 18

Answer: A) 18

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