[" 39.If "p,q,r" are not in G.P.and "],[qquad [1,(q)/(p)quad alpha+(q)/(p)],[1,(r)/(q)quad alpha+(r)/(q)],[p alpha+qquad q alpha+r,0]=0]

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 tan alpha = (q)/(p) and alpha lt 90^(@) ," then " (q sin alpha - p cos alpha )/( q sin alpha + p cos alpha ) =

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

The solution of equation (p+q-x)/(r)+(q+r-x)/(p)+(r+p-x)/(q)+(3x)/(p+q+r)=0 is

If (p)/( q - r) = (p + q)/( r) = (q)/( p) , Then find q : p : r

Add p(p-q),q(q-r) and r(r-p)