已知（m-1)^2+|m+n|=0,求4m^2+6n^2-mn-2m^2+5n^2-3mn的值

题目

已知（m-1)^2+|m+n|=0,求4m^2+6n^2-mn-2m^2+5n^2-3mn的值

答案

（m-1)²+|m+n|=0
m-1=0 m+n=0
m=1 n=-1
于是
4m²+6n²-mn-2m²+5n²-3mn
=4m²-2m²+5n²+6n²-mn-3mn
=2m²+11n²-4mn
=2×1²+11×(-1)²-4×1×(-1)
=2+11+4
=17