若x/3=y/2=z/5,且xy+yz+zx=93,求9x*x+12y*y+2z*z的值.

题目

若x/3=y/2=z/5,且xy+yz+zx=93,求9x*x+12y*y+2z*z的值.

答案

xy+yz+zx=93中的y,z全用x代替
可以得到2x^2/3+10x^2/9+5x^2/3=93
∴x^2=27
同理y^2=12 z^2=75
∴9x*x+12y*y+2z*z
=9*27+12*12+2*75
=537