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If a + b = 5 and a^2 + b^2 = 11,then prove that a^3 + b^3 = 20

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

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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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