Question 1121372
if y is the mean proportional between x and z ;
We know:
{{{x/y}}} = {{{y/z}}}; {{{y = sqrt(xz)}}}
:
 show that xy + yz is the mean proportional between x² + y² and y² + z²
{{{(x^2+y^2)/(xy+zy)}}} = {{{(xy+zy)/(y^2+z^2)}}}
The easiest to show this is to give some values to x & z
x=2; z=18; then y = {{{sqrt(2*18)}}} = 6 
:
{{{(4+36)/(12+108)}}} = {{{(12+108)/(36+324)}}}
{{{40/120}}} = {{{120/360}}}