Question

If p, q, r are in A.P., then(p+q-r) (q+r-p) is​

Answer 1

Step-by-step explanation:

$\\ As \: we \: know \: if \: p,q,r \: are \: in \: AP , \\</p><p>2q = p+r \\</p><p></p><p>Now \: let's \: Focus \: what \: we \: have \: to \: calculate.. \\ \\ </p><p>(p+q-r) (q+r-p) \\ \\ (p - r + \frac{p + r}{2} )(r - p + \frac{p + r}{2} ) \\ \\ ( \frac{2p - 2r + p + r}{2} )( \frac{2r - 2p + p + r}{2} ) \\ \\ ( \frac{3p - r}{2} )\times( \frac{3r - p}{2} ) \\ \\ ( \frac{9pr - 3 {p}^{2} - 3 {r}^{2} + pr }{4} ) \\ \\ \boxed{( \frac{10pr - 3 {p}^{2} - 3 {r}^{2} }{4} )}$

Answer 2

Step-by-step explanation:

now p,q,r are in A.P

then we assume p=1, q=2, r=3

(p+q-r)(q+r-p)=(1+2-3)(2+3-1)=0