If a2 + b2 = 117 and ab = 54, then (a + b)/(a - b) is(a) 3 (b) 5 (c)

1.	If a2 + b2 = 117 and ab = 54, then (a + b)/(a - b) is(a) 3 (b) 5 (c) 6 (d) 4
Answer» (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 ∴ \(\frac{a+b}{a-b} = \frac{15}{3}=5.\)

If a2 + b2 = 117 and ab = 54, then (a + b)/(a - b) is(a) 3 (b) 5 (c) 6 (d) 4

Answer»

(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

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