Question 7
Let $x,y,z$ be strictly positive real numbers such that
$$x+y+z\ge\frac1x+\frac1y+\frac1z.$$
Show that
$$\frac xy+\frac yz+\frac zx\ge\frac1{xy}+\frac1{yz}+\frac1{zx}.$$
$$x+y+z\ge\frac1x+\frac1y+\frac1z.$$
Show that
$$\frac xy+\frac yz+\frac zx\ge\frac1{xy}+\frac1{yz}+\frac1{zx}.$$