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[不等式] x,y,z的三种不等式的限制下求取值范围

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hbghlyj posted 2021-4-2 16:36 |Read mode
(1)x⩾y⩾z>0,则$1\le\left(\frac{y}{(x+y) (y+z)}+\frac{z}{(x+z) (y+z)}\right) (x+y+z) \le\frac32$.
(2)y⩾x⩾z>0,则$1\le\left(\frac{y}{(x+y) (y+z)}+\frac{z}{(x+z) (y+z)}\right) (x+y+z)\le\frac{25}{16}$.
(3)y⩾z⩾x>0,则$\frac32\le\left(\frac{y}{(x+y) (y+z)}+\frac{z}{(x+z) (y+z)}\right) (x+y+z)\le2$.

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