gt \Leftrightarrow \frac{1}{bc}+\frac{1}{ca}+\frac{1}{ab}=1 (1)đặt x=\frac{1}{a};y=\frac{1}{b};z=\frac{1}{c} (x,y,z>0 )
(1) \Leftrightarrow xy+yz+zx=1
VT of đpcm TT
\frac{1}{\sqrt{1+\frac{1}{x^{2}}}}+\frac{1}{\sqrt{1+\frac{1}{y^{2}}}}+\frac{1}{\sqrt{1+\frac{1}{z^{2}}}}
ta có \frac{1}{\sqrt{1+\frac{1}{x^{2}}}}=\frac{1}{\sqrt{\frac{x^{2}+1}{x^{2}}}}=\frac{x}{\sqrt{(x+y)(x+z)}} ( do xy+yz+zx=1)
\leq \frac{1}{2}(\frac{x}{x+y}+\frac{x}{x+z})
TT \Rightarrow VT\leq \frac{3}{2}
dấu "=" \Leftrightarrow a=b=c=\sqrt{3}