Find the mean proportional between `(x-y)` and `( x^3 - x^2y)`

Find the mean proportional between (x-y) and (x^(3)-x^(2)y)

Find the mean proportional to x - y and (x-y)^(3)

If y is the mean proportional between x and z , show that xy + yz is the mean proportional between x^(2) + y^(2) and y^(2) + z^(2).

If y is the mean proportional between x and z, prove that : (x^(2) - y^(2) + z^(2))/(x^(-2) - y^(-2) + z^(-2)) = y^(4) .

Find the : (i) fourth proportional to 2xy , x^(2) and y^(2) . (ii) third proportional to a^(2) - b^(2) and a + b . (iii) mean proportion to (x - y) and (x^(3) - x^(2)y)

Find the third proportional to (x^(2)-y^(2)) and (x+y)

6 is the mean proportional between two numbers x ad y and 48 is the third proportional of x and y. Find the numbers.