Non-zero numbers a and b satisfy a/b + b/a = 1. What is a³ + b³?

0. a/b + b/a = 1 gives a² + b² = ab, i.e. a² − ab + b² = 0. Then a³ + b³ = (a + b)(a² − ab + b²) = 0.

Non-zero numbers a and $b$ satisfy $a / b + b / a = 1$ . What is $a^{3} + b^{3}$ ?

Competition practiceAlgebra

a / b + b / a = 1

gives

a^{2} + b^{2} = ab

, i.e.

a^{2} - ab + b^{2} = 0

. Then

a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) = 0

Answer: A) 0

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