If a³ = 117 + b³ and a = 3 + b, then the value of a + b is:

Solution

a3 – b³ = 117 and a – b = 3 ⇒ a³ – b³ = (a – b) (a² + b² +ab) ⇒ 117 = 3 (a² + b² +ab) ⇒ 39 = a² + b² +ab ⇒ a² + b² = 39 – ab we Know that (a-b)² = a² +b² - 2ab                         = (a-b)² = 39 – ab – 2ab                         = (a-b)² = 39 – 3ab                   9    = 39 – 3ab = ab = 10 Now use (a+b)² = a² + b² + 2ab (a+b)² = 39 – ab + 2ab (a+b)² = 39 + ab = 39 + 10 (a+b)² = 49 = a + b = ±7