Question

If y is the mean proportion between x and z; show that xy+yz is the mean proportional between x square + y square and y square + z square.

Answer 1

Given that y is the mean proportion between x and z.
∴, y²=xz ----------------(1)
Now, (x²+y²)(y²+z²)
=(x²+xz)(xz+z²) [using (1)]
=xz(x+z)(x+z)
=xz(x+z)²
=y²(x+z)² [using (1)]
={y(x+z)}²
=(xy+yz)²
∴, (xy+yz) is the mean proportion of (x²+y²) and (y²+z²).