Question

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

(a) ± 7 

(b) 49 

(c) 0 

(d) ± 13

Answer 1

(a) ± 7

a³ = 117 + b³ ⇒ a³ - b³ = 117

a = 3 + b ⇒ a - b =3

⇒ 3³ = 117 - 3ab x 3

⇒ 27 = 117 - 9ab ⇒ 9ab = 90 ⇒ ab = 10

∴ Using the identity (a+b)² = (a - b)² = (a - b)² + 4ab, we have 

(a - b)² = 3² + 4 x 10 = 9 + 40 = 49

⇒ a + b = \(\sqrt{49}\) = ± 7.