[" 39If "p,q,r" are not in Gropand "1" q/p "x+2/p],[1quad x/qquad a+r/q=],[" partg quity "0],[" then prove that "pa^(2)+2qa+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 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 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 , prove that p : r = p^(2): q^(2) .

If p,q and r are in AP,then prove that (p+2q-r)(2q+r-p)(r+p-q)=4pqr

If p + r = 2q and 1/q + 1/s = 2/r , then prove that p : q = r : s .

If a/(q -r) = b/(r-p) = c/(p-q) , then prove that a + b + c = 0 =pa+ qb + rc .

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot