If √a + √b = 10 and √a - √b = 4, then what is the value of a + b?
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Correct answer: A
Explanation
Given:
√a + √b = 10
√a − √b = 4
According to the formula:
(a + b) = (√a + √b)² − 2√ab
(√a + √b)² = 100
(√a − √b)² = 16
(√a + √b)² + (√a − √b)² = 2(a + b)
100 + 16 = 2(a + b)
116 = 2(a + b)
a + b = 58