a/b + b/a = -1 ⇒ (a2 + b2)/(ab) = -1 a2 + ab + b2 = 0 Recall that a3 - b3 = (a - b)(a2 + ab + b2) Therefore, a3 - b3 = (a - b)(0) = 0

If a/b + b/a = -1, then a^3 - b^3 =?

Arturo O. answered • 05/22/18

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a/b + b/a = -1 ⇒

(a² + b²)/(ab) = -1

a² + ab + b² = 0

Recall that

a³ - b³ = (a - b)(a² + ab + b²)

Therefore,

a³ - b³ = (a - b)(0) = 0

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