若m,n是一元二次方程x²+2013x+7=0的两个实数根,试求(m²+2012m+6)(n²+2014n+8)的值
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![若m,n是一元二次方程x²+2013x+7=0的两个实数根,试求(m²+2012m+6)(n²+2014n+8)的值](/uploads/image/z/989984-56-4.jpg?t=%E8%8B%A5m%2Cn%E6%98%AF%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bx%26%23178%3B%2B2013x%2B7%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E8%AF%95%E6%B1%82%28m%26%23178%3B%2B2012m%2B6%29%EF%BC%88n%26%23178%3B%2B2014n%2B8%29%E7%9A%84%E5%80%BC)
若m,n是一元二次方程x²+2013x+7=0的两个实数根,试求(m²+2012m+6)(n²+2014n+8)的值
若m,n是一元二次方程x²+2013x+7=0的两个实数根,试求(m²+2012m+6)(n²+2014n+8)的值
若m,n是一元二次方程x²+2013x+7=0的两个实数根,试求(m²+2012m+6)(n²+2014n+8)的值
m是跟则x=m
则m²+2013m+7=0
所以m²+2012m+6=-m-1
同理
n²+2014n+8=n+1
且m+n=-2013
mn=7
所以原式=(-m-1)(n+1)
=-(mn+m+n+1)
=-(7-2013+1)
=2005