已知|x+2|+2(y-1/2)^2=0.求代数式3y^2-6x^2y-4y^2+2x^2y的值

题目

已知|x+2|+2(y-1/2)^2=0.求代数式3y^2-6x^2y-4y^2+2x^2y的值

答案

∵|x+2|≥0,(y-1/2)^2≥0,且|x+2|+2(y-1/2)^2=0
∴x+2=0,y-1/2=0 ==>x=-2,y=1/2
故3y^2-6x^2y-4y^2+2x^2y=-4x^2y-y^2
=-4(-2)^2*(1/2)-(1/2)^2
=8-1/4
=31/4.