Question

if P,Q,R are in A.P then p^2(q+r),q^2(r+p),r^2(p+q) are in​

Answer 1

Given :  P,Q,R are in A.P  

To find : P²(Q + R)   , Q²(R + P) ,  R²(P + Q)  are in

Solution:

P,Q,R are in A.P

=> 2Q = P + R

P²(Q + R)  

Q²(R + P)

R²(P + Q)

P²(Q + R)   + R²(P + Q)

= P²Q + P²R    + R²P + R²Q

= P²Q + R²Q  + PR(P + R)

=  P²Q + R²Q + PR(2Q)

=  Q(P² + R² + 2PR)

= Q(P + R)²

= Q(P + R)(P + R)

=Q(P + R)2Q

= 2Q²(P + R)

= 2Q²(R + P)

P²(Q + R)   + R²(P + Q)  = 2Q²(R + P)

=> P²(Q + R)   , Q²(R + P) ,  R²(P + Q) are in AP

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Answer 2

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