若x/3=y/2=z/5,且xy+yz+zx=93,求9x²+12y²+2z²的值.

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若x/3=y/2=z/5,且xy+yz+zx=93,求9x²+12y²+2z²的值.若x/3=y/2=z/5,且xy+yz+zx=93,求9x²+12y

若x/3=y/2=z/5,且xy+yz+zx=93,求9x²+12y²+2z²的值.
若x/3=y/2=z/5,且xy+yz+zx=93,求9x²+12y²+2z²的值.

若x/3=y/2=z/5,且xy+yz+zx=93,求9x²+12y²+2z²的值.
方法一:∵x/3=y/2=z/5
∴x=(3/2)y
z=(5/2)y
代入方程得: (3/2)y*y+y*(5/2)y+(5/2)y*(3/2)y=93 ∴y²=12
∴x²=27 z²=75 ∴9x²+12y²+2z²=537
方法二:(将它们都设为一个常数,方便计算)
设x/3=y/2=z/5=k
则x=3k,y=2k,z=5k
∵xy+yz+zx=93
∴6k²+10k²+15k²=93
∴k²=3
∴9x²+12y²+2z²=179k²=537
希望可以帮到你

x/3=y/2=z/5=k
x=3k,y=2k,z=5k
∵xy+yz+zx=93
∴6k²+10k²+15k²=93
k²=3
x²=27,y²=12,z²=75
9x²+12y²+2z²=27×9+12×12+2×75=537

答537

x=3/2 y ;
z=5/2 y;
xy+yz+zx=93 将x z 带入,解得 y平方=12
将x z 带入,即:
9(9/4)y方+12y方+2(25/4)y方=537