If a 2 + b 2 = 234 and ab = 108, find the value of (a + b) / (a - b).

Q: If a 2 + b 2 = 234 and ab = 108, find the value of (a + b) / (a - b).

We know that, (a + b)2 = a2 + b2 + 2ab = 234 + 2 x 108 = 450 (a - b)2 = a2 + b2 - 2ab = 234 - 2 x 108 = 18 ∴ (a + b)2/(a - b)2 = 450/18 = 25 ⇒ [(a + b)/(a - b)]2 = 25 ∴ (a + b)/(a - b) = √25 = 5

Correct Answer: 5

Explanation:

We know that, (a + b)² = a² + b² + 2ab
= 234 + 2 x 108 = 450
(a - b)² = a² + b² - 2ab
= 234 - 2 x 108 = 18
∴ (a + b)²/(a - b)² = 450/18 = 25
⇒ [(a + b)/(a - b)]² = 25
∴ (a + b)/(a - b) = √25 = 5

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