若X÷3=Y÷2=Z÷5,且XY+YZ+ZX=93,求9X二次方+12Y二次方+2Z二次方的值.

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若X÷3=Y÷2=Z÷5,且XY+YZ+ZX=93,求9X二次方+12Y二次方+2Z二次方的值.

若X÷3=Y÷2=Z÷5,且XY+YZ+ZX=93,求9X二次方+12Y二次方+2Z二次方的值.
若X÷3=Y÷2=Z÷5,且XY+YZ+ZX=93,求9X二次方+12Y二次方+2Z二次方的值.

若X÷3=Y÷2=Z÷5,且XY+YZ+ZX=93,求9X二次方+12Y二次方+2Z二次方的值.
令x/3=y/2=z/5=k,有x=3k,y=2k,z=5k,代入XY+YZ+ZX=93有:6k*k+10k*k+15k*k=31k*k=93
可解得:k*k=3.又有9x*x+12y*y+2z*z=81k*k+48k*k+50k*k=179k*k=537

令x/3=y/2=z/5=k,则有x=3k,y=2k,z=5k,代入XY+YZ+ZX=93有:6k*k+10k*k+15k*k=31k*k=93
可解得:k*k=3.所以9x*x+12y*y+2z*z=9*9k*k+12*4k*k+2*25k*k=179k*k=537

令x/3=y/2=z/5=k,,,有x=3k,y=2k,z=5k,代入XY+YZ+ZX=93有:6k*k+10k*k+15k*k=31k*k=93
可解得:k*k=3.又有9x*x+12y*y+2z*z=81k*k+48k*k+50k*k=179k*k=537

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