Question

If p,q & r are in A.P, then prove that (p+2q-r)(2q+r-p)(r+p-q) = 4pqr.

Answer 1

this is the answer for your questions

Answer 2

Answer:

If p,q & r are in A.P, then  (p+2q-r)(2q+r-p)(r+p-q) = 4pqr.

Step-by-step explanation:

If p,q & r are in A.P, then

$p+r=2q$

The given equation is

$(p+2q-r)(2q+r-p)(r+p-q)=4pqr$

Taking LHS,

$LHS=(p+2q-r)(2q+r-p)(r+p-q)$

$LHS=(p+p+r-r)(p+r+r-p)(2q-q)$           $[\because p+r=2q]$

$(p+2q-r)(2q+r-p)(r+p-q)=(2p)(2r)(q)$

$(p+2q-r)(2q+r-p)(r+p-q)=4pqr$

$(p+2q-r)(2q+r-p)(r+p-q)=RHS$

Hence proved LHS=RHS.