若实数x,y,z满足x+y+z=4[√(x-5)+√(y-4)+√(z-3)]求x,y,z的值
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若实数x,y,z满足x+y+z=4[√(x-5)+√(y-4)+√(z-3)]
求x,y,z的值
x+y+z=4[√(x-5)+√(y-4)+√(z-3)]
x-5-4√(x-5)+y-4-4√(y-4)+z-3-4√(z-3)+12=0
(√(x-5)-2)²+(√(y-4)-2)²+(√(z-3)-2)²=0
√(x-5)-2=0,得x=9
√(y-4)-2=0,得y=8
√(z-3)-2=0,得z=7
x+y+z=4[√(x-5)+√(y-4)+√(z-3)]
[(x-5)-2]^2+[√(y-4)-2]^2+[√(z-3)-2]^2=0
由非负数性质得:
[√(x-5)-2]^2=0,[√(y-4)-2]^2=0,[√(z-3)-2]^2=0
√(x-5)-2=0,√(y-4)-2=0,√(z-3)-2=0
x=9,y=8,z=7(x-5)-2]^2+[...
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x+y+z=4[√(x-5)+√(y-4)+√(z-3)]
[(x-5)-2]^2+[√(y-4)-2]^2+[√(z-3)-2]^2=0
由非负数性质得:
[√(x-5)-2]^2=0,[√(y-4)-2]^2=0,[√(z-3)-2]^2=0
√(x-5)-2=0,√(y-4)-2=0,√(z-3)-2=0
x=9,y=8,z=7
收起
[√(x-5)-2]^2=0,[√(y-4)-2]^2=0,[√(z-3)-2]^2=0
√(x-5)-2=0,√(y-4)-2=0,√(z-3)-2=0
x=9,y=8,z=7
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