已知a^(2/3)+b^(2/3)=4 x=a+3a^(1/3)b^(2/3) y=b+3a^(2/3)b(1/3) 求(x+y)^(2/3)+(x-y)^(2/3)求(x+y)^(2/3)+(x-y)^(2/3)
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已知a^(2/3)+b^(2/3)=4 x=a+3a^(1/3)b^(2/3) y=b+3a^(2/3)b(1/3) 求(x+y)^(2/3)+(x-y)^(2/3)求(x+y)^(2/3)+(x-y)^(2/3)
已知a^(2/3)+b^(2/3)=4 x=a+3a^(1/3)b^(2/3) y=b+3a^(2/3)b(1/3) 求(x+y)^(2/3)+(x-y)^(2/3)
求(x+y)^(2/3)+(x-y)^(2/3)
已知a^(2/3)+b^(2/3)=4 x=a+3a^(1/3)b^(2/3) y=b+3a^(2/3)b(1/3) 求(x+y)^(2/3)+(x-y)^(2/3)求(x+y)^(2/3)+(x-y)^(2/3)
x+y=a+3a^(1/3)b^(2/3) +b+3a^(2/3)b(1/3)
=(a^1/3)³+3a^(2/3)b(1/3)+3a^(1/3)b^(2/3)+(b^1/3)³
=(a^1/3+b^1/3)³
∴(x+y)^(2/3)=〔(a^1/3+b^1/3)³〕^2/3=(a^1/3+b^1/3)²
=a^(2/3)+2a^(1/3)b^(1/3)+b^(2/3)
=4+2a^(1/3)b^(1/3)
x-y=a+3a^(1/3)b^(2/3) -b-3a^(2/3)b(1/3)
=(a^1/3)³-3a^(2/3)b(1/3)+3a^(1/3)b^(2/3)-(b^1/3)³
=(a^1/3-b^1/3)³
∴(x-y)^(2/3)=〔(a^1/3-b^1/3)³〕^2/3=(a^1/3-b^1/3)²
=a^(2/3)-2a^(1/3)b^(1/3)+b^(2/3)
=4-2a^(1/3)b^(1/3)
∴(x+y)^(2/3)+(x-y)^(2/3)=4+2a^(1/3)b^(1/3)+4-2a^(1/3)b^(1/3)=8
说明:和的立方公式:(a+b)³=a³+3a²b+3ab²+b³
差的立方公式:(a-b)³=a³-3a²b+3ab²-b³
前面就是利用这两公式倒过来进行了因式分解.
请问你有抄错题吗?