Question

If $p,q$ and $r$ in $AP$, then prove that $(p+2q-r)(2q+r-p)(r+p-q)=4pqr$.

Answer 1

$p,q$ and $r$ are in $AP$

i.e., $2q=p+r$

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

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

$=\left(2p\right)\left(2r\right)\left(q\right)$

$=4pqr$

Hence proved