Question 4
Prove that, for all real numbers $x,y,z\in[1,2]$,
$$(x+y+z)\left(\frac1x+\frac1y+\frac1z\right)\ge6\left(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}\right).$$
Determine exactly when equality holds.
$$(x+y+z)\left(\frac1x+\frac1y+\frac1z\right)\ge6\left(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}\right).$$
Determine exactly when equality holds.