If a³ + b³ = 110 and a + b = 5, then (a + b)² – 3ab is equal to

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