高一数学函数的单调性请详细解答,谢谢! (1 12:4:19)

显示全部楼层 · 2009-8-1 12:08:34

(x+y)(x^3+y^3)=（x+y）（x+y）（x^2-xy+y^2）=（x+y）^2*[（x-y/2）^2+3y^2/4]因为（x-y/2）^2>=03y^2/4>=0所以[（x-y/2）^2+3y^2/4]因为（x+y）^2>=0所以（x+y）^2*[（x-y/2）^2+3y^2/4]>=0所以(x+y)(x^3+y^3) >=0...

千问 · 2009-8-1 12:08:34

(x+y)(x^3+y^3)=（x+y）（x+y）（x^2-xy+y^2）=（x+y）^2*[（x-y/2）^2+3y^2/4]所以(x+y)(x3+y3)>=0...

千问 · 2009-8-1 12:08:34

(x+y)(x3+y3)=x4+y4+xy3+yx3x4+y4≥2*x2y2≥0xy3+yx3=xy(x2+y2)
x2+y2≥2xy
xy(x2+y2)≥2*x2y2≥0所以(x+y)(x3+y3)≥4*x2y2≥0...

千问 · 2009-8-1 12:08:34

(x+y)(x3+y3)=(x+y)(x+y)(x2-xy+y2)=(x+y) 2 [(x-y/2) 2+3y2/4]≥0...

千问 · 2009-8-1 12:08:34

x3+y3=(x+y)(x2-xy+y2)所以(x+y)(x3+y3)=(x+y)2(x2-xy+y2)显然(x+y)2>=0x2-xy+y2=x2-xy+y2/4+3y2/4=(x-y/2)&...

高一 数学 函数的单调性 请详细解答,谢谢! (1 12:4:19)

高一数学函数的单调性请详细解答,谢谢! (1 12:4:19)