大师作文网一道数学题,有难度哦.
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/09/28 09:18:43
一道数学题,有难度哦.
若a = 三次根号4+三次根号2+三次根号1,求3/a+3/axa(两个a相乘的啊）+1/axaxa(三个a相乘)的值是?
若a = 三次根号4+三次根号2+三次根号1,求3/a+3/axa(两个a相乘的啊）+1/axaxa(三个a相乘)的值是?
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
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