If a + b = 5 and a2 + b2 = 11,then prove that a3 + b3 = 20 – InterviewSolution

1.

If a + b = 5 and a2 + b2 = 11,then prove that a3 + b3 = 20

Answer»

Given a + b = 5 and

a² + b² = 11

(a + b)² = (5)²

a² + b² + 2ab = 25

11 + 2ab = 25

2ab = 14

ab = 7

a³ + b³ = (a + b) (a² + b² – ab)

= 5(11 – 7)

= 5 × 4 = 20

∴ a³ + b³ = 20.

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