C1: $\sqrt{x^2+\frac 1{x^2}}+\sqrt{y^2+\frac 1{y^2}}+\sqrt{z^2+\frac 1{z^2}} \overset{Minkowski}\ge \sqrt{(x+y+z)^2+ \left( \frac 1x+\frac 1y+\frac 1z \right)^2 } $$\overset{C-S}\ge \sqrt{(x+y+z)^2+\frac{1}{(x+y+z)^2}+\frac{80}{(x+y+z)^2}} \ge \sqrt{2+80}=\sqrt{82}$
C2: $\sqrt{(1+81) \left( x^2 +\frac {1}{x^2} \right)} \overset{C-S}{\ge} x+\frac 9x$
Tương tự $\Rightarrow \sqrt{82}VT \ge x+y+z+\frac 9x+\frac 9y+\frac 9z \ge (x+y+z)+\frac{1}{x+y+z}+\frac{80}{x+y+z} \ge82$
$\Rightarrow$ dpcm
C3: $\sqrt{x^2+\frac 1{x^2}} \overset{\text{BDTD}}\ge \frac{-80x+54}{\sqrt{82}}$
Tương tự cộng lại có ngay dpcm