If c is the harmonic mean between a and b, then show that `(c ) /(a)+(c )/(b)=2`

If b is the harmonic mean between a and c, then prove that (1)/(b-a)+(1)/(b-c)=(1)/(a)+(1)/(c)

If b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(b) + (1)/(c)

If a,b,andc are in G.P.and x,y, respectively,are the arithmetic means between a,b, and b,c ,then the value of (a)/(x)+(c)/(y) is 1 b.2 c.1/2 d.none of these

If a,b, and c are in G.P.and x and y respectively,be arithmetic means between a,b, and b,c, then (a)/(x)+(c)/(y)=2b(a)/(x)+(c)/(y)=(c)/(a) c.(1)/(x)+(1)/(y)=(2)/(b) d.(1)/(x)+(1)/(y)=(2)/(ac)

If a is the A.M. between b and c, b the G.M. between a and c, then show that 1/a,1/c,1/b are in A.P.

If a, b, c are in G.P. then show that b^(2 ) = a.c.

If a, b, c are in AP, x is the GM between a and b, y is the GM between b and c, then show that b^(2) is the AM between x^(2) and y^(2) .

If a,b,c are in G.P., then show that a(b-c)^2=c(a-b)^2