If a² + b² = 148 and ab = 54, then find the value of (a + b) / (a - b).

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Accepted Answer

Given: a² + b² = 148 and ab = 54

We need to find (a + b) / (a - b).

Step 1: Use the identity (a + b)² = a² + 2ab + b²
=> (a + b)² = 148 + 2*54 = 148 + 108 = 256
=> a + b = √256 = 16 (taking positive root for simplicity)

Step 2: Use the identity (a - b)² = a² - 2ab + b²
=> (a - b)² = 148 - 2*54 = 148 - 108 = 40
=> a - b = √40 = 2√10

Step 3: Calculate (a + b) / (a - b) = 16 / (2√10) = 8 / √10

Therefore, the value is 8 / √10.

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