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)的算数平方根
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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)的算数平方根](/uploads/image/z/2494386-18-6.jpg?t=%E5%B7%B2%E7%9F%A5x%E3%80%81y%E5%9D%87%E4%B8%BA%E5%AE%9E%E6%95%B0%E4%B8%94%EF%BC%88x-y%EF%BC%89%26%23178%3B%E4%B8%8E%E2%88%9A%EF%BC%885x-3y-16%EF%BC%89%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E6%B1%822%EF%BC%88x%26%23178%3B%2By%26%23178%3B%EF%BC%89%E7%9A%84%E7%AE%97%E6%95%B0%E5%B9%B3%E6%96%B9%E6%A0%B9)
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)的算数平方根
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)的算数平方根
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)的算数平方根
(x-y)²与√(5x-3y-16)互为相反数
那么(x-y)²+√(5x-3y-16)=0
所以x-y=0且5x-3y-16=0
解得x=y=8
∴2(x²+y²)=2*(64+64)=256
∴√[2(x²+y²)]=16