If a & # 178; = a + 1, B & # 178; = B + 1, a ≠ B, then what is a ^ 5 + B ^ 5 equal to?

In fact, a and B are the two roots of the equation x ^ 2 = x + 1 (i.e., x ^ 2-x-1 = 0). According to the root formula, x = [1 ± √ (1 + 4)] / 2 = (1 ± √ 5) / 2, so if a is greater than B (in fact, a is less than B), then a = (1 + √ 5) / 2B = (1 - √ 5) / 2A ^ 5 = a ^ 2 * a ^ 2 * a = (a + 1) ^ 2 * a = (3 + √ 5) ^ 2 / 4 * (1 + √ 5) / 2 = (44 + 20 √

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