已知x,y∈[-1,1],则二元多项式P(x,y)=x^2+2xy+2y^2-y+1的取值范围是

题目

已知x,y∈[-1,1],则二元多项式P(x,y)=x^2+2xy+2y^2-y+1的取值范围是

答案

解由P(x,y)=x^2+2xy+2y^2-y+1=x^2+2xy+y^2+y²-y+1=（x+y）²+（y-1/2)²+3/4≥3/4即P(x,y)≥3/4当当y=-1,x=-1时P(x,y)有最大值=（x+y）²+（y-1/2)²+3/4=（-2）²+(-1-1/2）²+3/4=7...