If `5^(-p)=4^(-q)=20^(r)` show that `1/p+1/q+1/r=0`

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show that 1/p+1/r=2/q .

if a=xy^(p-1),b=xy^(q-1),c=xy^(r-1) show that a^(q-r).b^(r-p).c^(p-q)=1

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

(2) If a=x^(q+r)*y^(p) , b=x^(r+p)*y^(q) , c=x^(p+q)y^(r) , show that a^(q-r)b^(r-p)c^(p-q)=1

(a) If r^(2) = pq , show that p : q is the duplicate ratio of (p + r) : (q + r) . (b) If (p - x) : (q - x) be the duplicate ratio of p : q then show that : (1)/(p) + (1)/(q) = (1)/(r) .

If p,q,r three complex nos. so that p+q+r =0 and abs(p)=abs(q)=absr=1 then the value of (1/p+1/q+1/r) is

If pqr=1 show that (1)/(1+p+q^(-1))+(1)/(1+q+r^(-1))+(1)/(1+r+p^(-1))=1

If a=xy^(p-1),b=yz^(q-1),c=zx^(r-1) , then a^(q-r)b^(r-p)c^(p-q) is equal to

If x^(1/p)=y^(1/q)=z^(1/r) and xyz=1, then the value of p+q+r=