If a = 4 + √7, b = 4 − √7, then what is the value of a² + b²?
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Correct answer: B
Explanation
Given:
a = 4 + √7, b = 4 − √7
According to the formula:
(a + b)² = a² + b² + 2ab
a + b = (4 + √7) + (4 − √7) = 8
ab = (4 + √7)(4 − √7) = 16 − 7 = 9
(a + b)² = a² + b² + 2ab
8² = a² + b² + 2×9
64 = a² + b² + 18
a² + b² = 64 − 18 = 46