Question

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

Answer 1

Hope it helps you ...

Answer 2

Solution:

Given p,q and r are in A.P

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we know that ,

common difference of any two consecutive terms are equal in A.P.

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q-p = r-q

=> q+q = r+p

=> 2q = p+r -----(1)

Now ,

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

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

/* from (1) */

= (2p)×(2r)×q

= 4pqr

= RHS

Therefore,

If p,q and r are in A P, then

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

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