已知m,n都是方程x²+12x-2012=0的根,试求(m²+12m-12)(n²+12n+1988)的值
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![已知m,n都是方程x²+12x-2012=0的根,试求(m²+12m-12)(n²+12n+1988)的值](/uploads/image/z/2485399-31-9.jpg?t=%E5%B7%B2%E7%9F%A5m%2Cn%E9%83%BD%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B%2B12x-2012%3D0%E7%9A%84%E6%A0%B9%2C%E8%AF%95%E6%B1%82%EF%BC%88m%26%23178%3B%2B12m-12%29%EF%BC%88n%26%23178%3B%2B12n%2B1988%EF%BC%89%E7%9A%84%E5%80%BC)
已知m,n都是方程x²+12x-2012=0的根,试求(m²+12m-12)(n²+12n+1988)的值
已知m,n都是方程x²+12x-2012=0的根,试求(m²+12m-12)(n²+12n+1988)的值
已知m,n都是方程x²+12x-2012=0的根,试求(m²+12m-12)(n²+12n+1988)的值
∵m,n都是方程x²+12x-2012=0的根
∴m²+12m-2012=0,n²+12n-2012=0
∴m²+12m=2012,n²+12n=2012
∴(m²+12m-12)(n²+12n+1988)=(2012-12)×(2012+1988)
=2000×4000
=8000000
(m²+12m-12)(n²+12n+1988)=(m²+12m-2012+2000)(n²+12n-2012+4000)
=2000*4000=8000000
∵m,n都是方程x²+12x-2012=0的根
∴m^2+12m-2012=0 n^2+12n-2012=0
∴m^2+12m-12=2000 n^2+12n+1988=4000
∴(m^2+12m-12)*(n^2+12n+1988)=2000*4000=8000000