Question

如果m、n是两个不相等的实数，且满足m2-2m=1，n2-2n=1，那么代数式2m2+4n2-4n+1994=______

如果m、n是两个不相等的实数，且满足m2-2m=1，n2-2n=1，那么代数式2m2+4n2-4n+1994=______．

Answer 1

根据题意可知m，n是x²-2x-1=0两个不相等的实数根．
则m+n=2，
又m²-2m=1，n²-2n=1
2m²+4n²-4n+1994
=2（2m+1）+4（2n+1）-4n+1994
=4m+2+8n+4-4n+1994
=4（m+n）+2000
=4×2+2000
=2008．