[" If "a,b,cquad " are "quad " in "quad " AP,the prove that "],[(1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b))" are in AP."]

If a,b,c, are in A.P then prove that (1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b)) are in A.P.

Three positive numbers a, b, c are in A.P. Prove that (1)/(sqrt(b)+sqrt(c )), (1)/(sqrt(c )+sqrt(a)) , (1)/(sqrt(a) + sqrt(b)) are also in A.P.

If a, b, c are in A.P., prove that : 1/(sqrtb+sqrtc), 1/(sqrtc+sqrta), 1/(sqrta+sqrtb) are also in A.P.

If a, b, c are in A.P., prove that frac(1)(sqrtb+sqrtc),frac(1)(sqrtc+sqrta),frac(1)(sqrta+sqrtb) are also in A.P.

If a,b,c are in A.P. prove that (i) b+c,c+a,a+b are also in A.P. (ii) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b)) are also in A.P.

Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc) , 1/(sqrtc+sqrta) and 1/(sqrta+sqrtb) are aslo in A.P

If a,b,c are in AP,then prove that (a-c)^(2)=4(b^(2)-ac)

If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac) .

If a ,b ,c are in A.P., then prove that: (a – c)^2 = 4(b^2 – ac).