Bài này mình xin làm, chắc kiến thức này lớp 8 vẫn hiểu:
Bđt $\Leftrightarrow \frac{xyz+1}{xy+x}+\frac{xyz+1}{yz+y}+\frac{xyz+1}{zx+z}\geq 3\Leftrightarrow \frac{xyz+1}{xy+x}+1+\frac{xyz+1}{yz+y}+1+\frac{xyz+1}{zx+z}+1\geq 6\Leftrightarrow \frac{xyz+1+xy+x}{x(y+1)}+\frac{xyz+1+yz+y}{y(z+1)}+\frac{xyz+1+xz+z}{z(x+1)}\geq 6\Leftrightarrow \frac{xy(z+1)+(x+1)}{x(y+1)}+\frac{yz(x+1)+(y+1)}{y(z+1)}+\frac{zx(y+1)+(z+1)}{zx(x+1)}=\frac{y(z+1)}{y+1}+\frac{x+1}{x(y+1)}+\frac{z(x+1)}{z+1}+\frac{y+1}{y(z+1)}+\frac{z(x+1)}{z+1}+\frac{y+1}{y(z+1)}\geq 6$ (Áp dụng bđt AM-GM cho 6 số).Vấn đề đã đc giải quyết
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