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

(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 6!=2^(p)3^(q)5^(r) then ,p+q+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 a, b, c be respectively the sums of p, q, r terms of an A.P., show that, (a)/(p)(q-r) + (b)/(q)(r-p) +(c )/(r )(p-q) = 0

If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p/(p-a)+q/(q-b)+r/(r-c)=2 .

The sum of first p.q.r terms of an AP are a;b;c respectively.Show that a(q-r)/(p)+b(r-p)/(q)+c(p-q)/(r)=0

The sum of the first p,q,r terms of an A.P.are a,b,c respectively.Show that (a)/(p)(q-r)+(b)/(q)(r-p)+(c)/(r)(p-q)=0

The sum of the first p,q, rterms of an A.P are a,b, crespectively.Show that (a)/(p)[q-r]+(b)/(q)[r-p]+(c)/(r)[p-q]=0

Consider f:{4,5,6}->{p ,q, r} given by f(4)=p , f(5)=q and f(6)=r . Find f^(-1) and show that (f^(-1))^(-1)=f .

Show that (pvvq) to r -= (p to r) ^^ (q to r)