[" If "5^(-p)=4^(-q)=20^(r);" show that: "],[qquad (1)/(p)+(1)/(q)+(1)/(r)=0]

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

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

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

(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

if q is the mean proportional between p and r , prove that : p^(2) - q^(2) + r^(2) = q^(4) ((1)/(p^(2))-(1)/(q^(2)) + (1)/(r^(2))) .

If A=((p,q),(0,1)) , then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(0,1))

If A=((p,q),(0,1)) , then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(0,1))