Find the mean proportional between a - b and a³ - a²b

If x + 5 is the mean proportion between x + 2 and x + 9; find the value of x.

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x² + y² and y² + z².

If q is the mean proportional between p and r, show that :

pqr(p + q + r)³ = (pq + qr + pr)³.