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?
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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?
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?
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?
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
a = 三次根号4+三次根号2+三次根号1
= ³√4 + ³√2 + ³√1
= ³√2² + ³√2 + 1
= (³√2² + ³√2 + 1)(³√2 - 1)/(³√2 - 1)
= (³√2³ - 1)/(³√2...
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a = 三次根号4+三次根号2+三次根号1
= ³√4 + ³√2 + ³√1
= ³√2² + ³√2 + 1
= (³√2² + ³√2 + 1)(³√2 - 1)/(³√2 - 1)
= (³√2³ - 1)/(³√2 - 1)
= (2 - 1)/(³√2 - 1)
= 1 /(³√2 - 1)
3/a+3/axa(两个a相乘的啊）+1/axaxa(三个a相乘)
= 3(³√2 - 1)+3(³√2 - 1)²+(³√2 - 1)³
= [1 + 3(³√2 - 1)+3(³√2 - 1)²+(³√2 - 1)³] - 1
= (1 + ³√2 - 1)³ - 1
= (³√2)³ - 1
= 2 - 1
= 1
收起
1
1
a=4^1/3+2^1/3+1==>a+1=2+4^1/3+2^1/3=a*2^1/3==>(a+1)^3=2a^3
即
a^3+3a^2+3a+1=2a^3
3a^2+3a+1=a^3
原式=3/a+3/a^2+1/a^3=(3a^2+3a+1)/a^3=1