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

Let a, b, c be in AP. Consider the following statements: 1. (1)/(ab),(1)/(ca)" and "(1)/(bc)" are in AP." 2. (1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a))" and "(1)/(sqrt(a)+sqrt(b))" are in AP." Which of the statements given above is/are correct?

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

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

If (1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b)) are in A.P.,then 9^(9x+1),9^(bx+1),9^(cx+1),x!=0 are in

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

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in