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/(b + c), b/(c + a), c/(a + b) are in A.P., then

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

If a ,b ,ca n dd are in H.P., then prove that (b+c+d)//a ,(c+d+a)//b ,(d+a+b)//c and (a+b+c)//d , are in A.P.

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^2, b^2,c^2 are in A.P., then prove that tanA ,tanB ,tanC are in H.P.

If a, b, c are in A.P. then show that 3^(a), 3^(b), 3^(c) are in G.P.

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)

a ,b ,c are positive real numbers forming a G.P. ILf a x 62+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

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)