Find the mean - proportional of `(a + b)^(2)" and " (a - b)^(2)`.

Explanation

Let the mean - proportional of `(a+b)^(2) " and " (a - b)^(2) ` be x.
` :. ((a +b)^(2))/x = x/((a-b)^(2))`
or, ` x^(2) = ( a + b)^(2) xx (a - b)^(2)`
or, ` x^(2) = {(a + b)(a - b)^(2) " or, " x^(2) = (a^(2) - b^(2))^(2)`.
or, ` x = pm(a^(2) - b^(2))`
Hence the required mean - proportional `= pm (a^(2) - b^(2))`.