Question

If a² + b² = 117 and ab = 54, then (a + b)/(a - b) is

(a) 3 

(b) 5 

(c) 6 

(d) 4

Answer 1

(b) 5

(a + b)² = a² + b² + 2ab = 117 + 108 = 225

⇒ a + b = 15

(a + b)² = a² + b² + 2ab = 117 - 108 = 9

⇒ a - b = 3

∴ \(\frac{a+b}{a-b} = \frac{15}{3}=5.\)