若有理数a,b,c满足:(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,求a+b+c的值
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![若有理数a,b,c满足:(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,求a+b+c的值](/uploads/image/z/3942032-32-2.jpg?t=%E8%8B%A5%E6%9C%89%E7%90%86%E6%95%B0a%2Cb%2Cc%E6%BB%A1%E8%B6%B3%EF%BC%9A%EF%BC%88a%EF%BC%8D1%EF%B9%9A%26%23178%3B%EF%BC%8B%EF%B9%992a%EF%BC%8Db%EF%B9%9A%26%23178%3B%EF%BC%8B%7Ca%EF%BC%8D3c%7C%EF%B9%A60%2C%E6%B1%82a%2Bb%2Bc%E7%9A%84%E5%80%BC)
若有理数a,b,c满足:(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,求a+b+c的值
若有理数a,b,c满足:(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,求a+b+c的值
若有理数a,b,c满足:(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,求a+b+c的值
因为(a-1)²>=0,﹙2a-b﹚²>=0,|a-3c|>﹦0,
要使(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,
则(a-1)²=0,解得a=1
且﹙2a-b﹚²=0,解得2-b=0,b=2
且|a-3c|﹦0,解得1-3c=0,c=1/3
a+b+c
=1+2+1/3
=10/3
希望能够帮助你,有疑问欢迎追问,
∵(a-1﹚²+﹙2a-b﹚²+|a-3c|﹦0,
∴(a-1﹚²=0,﹙2a-b﹚²=0, |a-3c|﹦0,
a-1=0, 2a-b=0, a-3c=0
解得:a=1, b=2, c=1/3
∴a+b+c
=1+2+(1/3)
=10/3.