(1 + √5)² + (1 − √5)² − 6 = ?
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Correct answer: D
Explanation
Given:
(1 + √5)² + (1 − √5)² − 6
According to the formulas:
(a + b)² = a² + b² + 2ab
(a − b)² = a² + b² − 2ab
(1 + √5)² = 1 + 5 + 2√5 = 6 + 2√5
(1 − √5)² = 1 + 5 − 2√5 = 6 − 2√5
Sum = (6 + 2√5) + (6 − 2√5) = 12
12 − 6 = 6