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 a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

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

If a,b,c are in A.P., then prove that the following are also in A.P (i) a^(2)(b+c),b^(2)(c+a),c^(2)(a+b) ltbr gt(ii) 1/(sqrtb+sqrtc),1/(sqrtc+sqrta),1/(sqrta+sqrtb) (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)

If x, y, z are in A.P then 1/(sqrt(x) + sqrt(y)) , 1/(sqrt(z) + sqrt(x)) , 1/(sqrt(y) + sqrt(z)) are in

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

3 circles of radii a,b,c (a

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

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(a c),c+1//(a b) are also in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

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