Question

If a + b = 11 and a² + b² = 65; find a³ + b³.

Answer 1

a + b = 11 and a2 + b2 = 65
Now, (a+b)² = a² + b² + 2ab
⇒ (11)² = 65 + 2ab
⇒ 121 = 65 + 2ab
⇒  2ab = 56
⇒  ab = 28

a³ + b³ = ( a + b )( a² - ab + b2)
             = (11)(65 - 28)
             = 11 x 37
             = 407