已知x-y=m,z-y=20,求x²+y²+z²-xy-yz-zx的最小值
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已知x-y=m,z-y=20,求x²+y²+z²-xy-yz-zx的最小值已知x-y=m,z-y=20,求x²+y²+z²-xy-yz-zx的最小值已知
已知x-y=m,z-y=20,求x²+y²+z²-xy-yz-zx的最小值
已知x-y=m,z-y=20,求x²+y²+z²-xy-yz-zx的最小值
已知x-y=m,z-y=20,求x²+y²+z²-xy-yz-zx的最小值
x-y=m,z-y=20可得:
x-z=(x-y)-(z-y)=m-20
x²+y²+z²-xy-yz-zx
=(2x²+2y²+2z²-2xy-2yz-2zx)/2
=[(x-y)²+(z-y)²+(x-z)²]/2
=[m²+20²+(m-20)²]/2
=m²-20m+400
=m²-20m+100+300
=(m-10)²+300≥300
所以最小值为300
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