ABC≠0和1，x、y、z为整数，且x+y+z=0,A的(yz)次方=B的(xz)次方yz=C的(xy)次方,求证：ABC=-1.
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ABC≠0和1，x、y、z为整数，且x+y+z=0,A^(yz)=B^(xz)=C^(xy),求证：ABC=-1.当x=y=z=0时，A、B、C可以不满足 ABC=-1 当xyz≠0时，设 |A^(yz)|=|B^(xz)|=|C^(xy)|＝k则 lgk = (yz)*lg|A| = (xz)*lg|B| = (xy)*lg|C|所以lg|A|= lgk/(yz) ,lg|B|= lgk/(xz) ,lg|C|=lgk/(xy)相加得：lg|ABC|= lgk/(yz)+lgk/(xz)+lgk/(xy)即 lg|ABC| = (x+y+z)*lgk/(xyz) = 0所以 |ABC|=1 ,所以由已知得：ABC=-1 |