Question

Find mean proportional of `( x + y)/( x - y), (x^2 - y^2)/(x^2y^2)`

Answer 1

If b is the mean proportional of a and c, then `b^2 = ac`

Mean proportional of `[ x + y]/[ x - y] and [ x^2 - y^2]/[ x^2y^2]`

`therefore b^2 = [x + y]/[x - y] xx [ x^2 - y^2]/[x^2y^2]`

`b^2 = [x + y]/[x -y] xx [( x - y)( x + y)]/( x^2y^2)`

`therefore b^2 = [(x + y)^2]/(xy)^2`

`therefore b = [x + y]/(xy)`