If a + b = √17 and a - b = √1, find (a² + b²) / (ab).
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Correct answer: A
Explanation
Given:
a + b = √17
a − b = √1
By the formula:
(a + b)² = a² + b² + 2ab
(a − b)² = a² + b² − 2ab
(a + b)² = 17
(a − b)² = 1
17 + 1 = 2(a² + b²)
18 = 2(a² + b²)
a² + b² = 9
17 − 1 = 4ab
16 = 4ab
ab = 4
Now
(a² + b²) / ab = 9 / 4