若2^(6x)=3^(3y)=6^(2z)求证3xy-2xz-yz=0
来源:百度知道 编辑:UC知道 时间:2024/05/28 10:53:43
2^6x=3^3y=6^2z=(2*3)^2z=2^2z*3^2z
====2^6x=2^2z*3^2z
====2^(6x-2z)=3^2z (等式两边同时取对数)
====(6x-2z)lg2=2zlg3 @
同理:(3y-2z)lg3=2zlg2 @
6xlg2=3ylg3 @
联立三个@,化简解得:
y/2x=z/(3x-z)=(3y/z)-1
同乘2xy(3x-z)得:
2xz^2=zy(3x-z)=3yz(3x-z)-2xz(3x-z)
则:zy=3yz-2xz
即:3yz-2xz-zy=0
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3(x+y)(x-y)+4(x-y)^2=?
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