Toán 9 Bất đẳng thức

đpcm <=> [tex]\frac{1}{(\frac{1}{x}+y)^2}+\frac{1}{(\frac{1}{y}+z)^2}+\frac{1}{(\frac{1}{x}+z)^2}\geq \frac{3}{4}[/tex]
[tex]<=> \sum \frac{1}{y^2}\frac{1}{(z+1)^2} \geq \frac{3}{4}[/tex]
Đặt[tex]x=\frac{a}{b} , y=\frac{b}{c} , z=\frac{c}{a}[/tex]
VT= [tex]\frac{(ac)^2}{(bc+ac)^2}+\frac{(bc)^2}{(ab+ac)^2}+\frac{(ab)^2}{(bc+ac)^2}\geq 3(\frac{ac}{bc+ac}+\frac{bc}{ab+ca}+\frac{ab}{bc+ac})^2\geq \frac{1}{3}\frac{3^2}{2^2}=\frac{3}{4}[/tex]