已知x、y均为实数,且(x-y)²与√5x-3y-16互为相反数,求2(x²+y²)的算术平方根.
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已知x、y均为实数,且(x-y)²与√5x-3y-16互为相反数,求2(x²+y²)的算术平方根.
已知x、y均为实数,且(x-y)²与√5x-3y-16互为相反数,求2(x²+y²)的算术平方根.
已知x、y均为实数,且(x-y)²与√5x-3y-16互为相反数,求2(x²+y²)的算术平方根.
(x-y)²≥0
√5x-3y-16≥0
(x-y)²与√5x-3y-16互为相反数,所以
(x-y)²=0,得x=y
5x-3y-16=0,
2y-16=0
得y=8
x=y=8
√2(x²+y²)=√256=16