已知x,y属于R,x²-2xy+2y²=2,求x+y的取值范围
问题描述:
已知x,y属于R,x²-2xy+2y²=2,求x+y的取值范围
答
t = x + y,x = t - yx²-2xy+2y² = x² + 2xy + y² - 4xy + y²= (x + y)² - 4xy + y²= t² - 4(t - y)y + y²= t² - 4yt + 5y² = 2t² - 4yt + 5y² - ...