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

If p+(1)/(p)=q, then for p>0

If p - q is small compared to either p or q, then show that sqrt(p/q)=((n+1)p+(n-1)q)/((n-1)p+(n+1)q) Hence find sqrt(15/16) .

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 p xx q=p+q+(p)/(q) then 8xx2

If the roots of the equation (1-q+(p^(2))/(2))x^(2)+p(1+q)x+q(q-1)+(p^(2))/(2)=0 are equal then show that p^(2)=4q

(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) .