若x:y:z=3:1:2,且zx-xy-yz=99,求2x^2+12y^2+9z^2的值
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若x:y:z=3:1:2,且zx-xy-yz=99,求2x^2+12y^2+9z^2的值若x:y:z=3:1:2,且zx-xy-yz=99,求2x^2+12y^2+9z^2的值若x:y:z=3:1:2
若x:y:z=3:1:2,且zx-xy-yz=99,求2x^2+12y^2+9z^2的值
若x:y:z=3:1:2,且zx-xy-yz=99,求2x^2+12y^2+9z^2的值
若x:y:z=3:1:2,且zx-xy-yz=99,求2x^2+12y^2+9z^2的值
x:y:z=3:1:2,
所以x/3=y/1=z/2
所以x=3y,z=2y
代入zx-xy-yz=99
6y^2-3y^2-2y^2=99
y^2=99
所以x^2=(3y)^2=9y^2
z^2=(2y)^2=4y^2
所以2x^2+12y^2+9z^2
=2*9y^2+12y^2+9*4y^2
=66y^2
=66*99
=6534
x:y:z=3:1:2
不妨设x=3k,y=k,z=2k
zx-xy-yz=99
2k×3k-3k×k-k×2k=99
6k²-3k²-2k²=99
k²=99
2x²+12y²+9z²
=2(3k)²+12k²+9(2k)²
=18k²+12k²+36k²
=66k²
=66×99
=6534
若x/3=y/1=z/2,且xy+yz+zx=99,求zx平方+9y平方+9z平方的值?
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