If a³ + b³ = 110 and a + b = 5, then (a + b)² – 3ab is equal to:
a) 52
b) 32
c) 42
d) 22
Sol:
a + b = 5
a³ + b³ = 110 ⇒ (a + b) (a² + b² – ab) = 110
a² + b² – ab = 22
a² + b² + 2ab – 3ab = 22
(a + b)² – 3ab = 22
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