Cho $$a, b, c >0$$. Tìm GTNN
$$P= \frac{4a}{a+b+2c}+\frac{b+3c}{2a+b+c}-\frac{8c}{a+b+3c}$$
Cho $$a, b, c >0$$. Tìm GTNN
$$P= \frac{4a}{a+b+2c}+\frac{b+3c}{2a+b+c}-\frac{8c}{a+b+3c}$$
Cho $$a, b, c >0$$. Tìm GTNN
$$P= \frac{4a}{a+b+2c}+\frac{b+3c}{2a+b+c}-\frac{8c}{a+b+3c}$$
Đặt: $x=a+b+2c;y=2a+b+c;z=a+b+3c$
Khi đó thì: $c=z-x;a=z+y-2x;b=5x-y-3z$
Thay vào thì: $P=-17+2(\frac{2y}{x}+\frac{x}{y})+4(\frac{2x}{z}+\frac{z}{x})\geq 12\sqrt{2}-17$
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