Question

If q is the mean proportion between p and r, then show that pqr ( p + q + r ) ^3 = ( pq + qr + pr )

Answer 1

By defintion q = (pr)1/2

Then pqr(p + q + r)3 = (pr) * (pr)1/2 *(p + q + r)3
= (pr)3/2(p + q + r)3
= ((pr)1/2*(p + q +r))3
= (q(p + q + r))3
=(pq + q2 + rq)3
= (pq + pr + rq)3

Answer 2

Your answer is given above.

Hope you find it helpful.