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已知 a=三次根号4+三次根号2+1.则3/a+3/a^2+1/a³=____
a = 4^(1/3) + 2^(1/3) + 1
令 x = 2^(1/3)
则 a = x² + x + 1
a (x - 1) = (x - 1)(x² + x + 1) = x³ - 1 = 2 - 1 = 1
所以:x = 1 + 1/a
3/a + 3/a² + 1/a³ = (1 + 1/a)³ - 1 ---------- 利用了:(1 + x)³ = 1 + 3x + 3x² + x³
= x³ - 1
= 2 - 1
= 1
.则 3/a + 3/a² + 1/a³ = __ 1 __
答案:1
1年前
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