已知实数a,b,c满足|a+1|+(b-5)^2+(25c^2+10c+1)=0,求(abc)^251/(a^11b^8c^7)的值
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![已知实数a,b,c满足|a+1|+(b-5)^2+(25c^2+10c+1)=0,求(abc)^251/(a^11b^8c^7)的值](/uploads/image/z/2703097-1-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0a%2Cb%2Cc%E6%BB%A1%E8%B6%B3%EF%BD%9Ca%2B1%EF%BD%9C%2B%EF%BC%88b-5%EF%BC%89%5E2%2B%2825c%5E2%2B10c%2B1%29%3D0%2C%E6%B1%82%28abc%29%5E251%2F%28a%5E11b%5E8c%5E7%29%E7%9A%84%E5%80%BC)
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已知实数a,b,c满足|a+1|+(b-5)^2+(25c^2+10c+1)=0,求(abc)^251/(a^11b^8c^7)的值
已知实数a,b,c满足|a+1|+(b-5)^2+(25c^2+10c+1)=0,求(abc)^251/(a^11b^8c^7)的值
已知实数a,b,c满足|a+1|+(b-5)^2+(25c^2+10c+1)=0,求(abc)^251/(a^11b^8c^7)的值
已知实数a,b,c满足|a+1|+(b-5)²+(25c²+10c+1)=0
|a+1|+(b-5)²+(5c+1)²=0
a+1=0,b-5=0,5c+1=0
所以a=-1,b=5,c=-1/5
所以(abc)^251/(a^11b^8c^7)
=[(-1)*5*(-1/5)]^251/[(-1)^11*5^8*(-1/5)^7]
=1/[(-1)*5*(-1)]
=1/5
|a+1|+(b-5)^2+(25c^2+10c+1)=0,
|a+1|>=0,(b-5)^2>=0,(25c^2+10c+1)>=0,
a+1=0,
b-5=0
25c^2+10c+1=(5c+1)²=0
a=-1,b=5,c=-1/5
(abc)^251/(a^11b^8c^7)
=1/5
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