If p, q, r are not in G.P. and `|[1,q/p,alpha+q/p],[1,r/p,alpha+r/q],[palpha+q,qalpha+r,0]|=0` Show that `palpha^2+2qalpha+r=0`

If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),(palpha+q,qalpha+r,0)|=0 then prove that palpha^2+2qalpha+r=0

If p,q,r are not in geometric progression and |[1,q/p,alpha+q/p],[1,r/q,alpha+r/q],[palpha+q,qalpha+r,0]|=0 then prove that palpha^2+2q alpha^2+r=0

If p,q,r are in H.P. and p,q,-2r are in G.P. ( p,q,r, gt0) then

If p,q,r,s are in G.P. show that (p+q),(q+r),(r+s) are also in G.P.

If p, q. r in G.P and 1/(p-a),1/(r-p),1/(q-r) are in AP.show that p+4q+r=0

p,q,q,r Show that ,q,p,,q,r,r,p,r,q

If alpha is complex fifth root of unity and (1+alpha +alpha^(2)+ alpha^(3))^(2005) = p + qalpha + ralpha^(2) + salpha^(3) (where p,q,r,s are real), then find the value of p+ q+r+s .

If alpha is complex fifth root of unity and (1+alpha +alpha^(2)+ alpha^(3))^(2005) = p + qalpha + ralpha^(2) + salpha^(3) (where p,q,r,s are real), then find the value of p+ q+r+s .

If p, q, r are in A.P the p^(2) (q + r), q^(2) (r + p), r^(2) (p+q) are in