已知实数m,n满足等式m2-m-根号3=0,n2-n-根号3=0,且m不等于n,求(mn)2-m-n
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![已知实数m,n满足等式m2-m-根号3=0,n2-n-根号3=0,且m不等于n,求(mn)2-m-n](/uploads/image/z/1763423-71-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0m%2Cn%E6%BB%A1%E8%B6%B3%E7%AD%89%E5%BC%8Fm2-m-%E6%A0%B9%E5%8F%B73%3D0%2Cn2-n-%E6%A0%B9%E5%8F%B73%3D0%2C%E4%B8%94m%E4%B8%8D%E7%AD%89%E4%BA%8En%2C%E6%B1%82%28mn%292-m-n)
已知实数m,n满足等式m2-m-根号3=0,n2-n-根号3=0,且m不等于n,求(mn)2-m-n
已知实数m,n满足等式m2-m-根号3=0,n2-n-根号3=0,且m不等于n,求(mn)2-m-n
已知实数m,n满足等式m2-m-根号3=0,n2-n-根号3=0,且m不等于n,求(mn)2-m-n
根据题意可知
m,n分别是方程x²-x-√3=0的两个不同实数解
于是
m+n=1
mn=-√3
从而
(mn)²-m-n
=(-√3)²-1
=3-1
=2