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 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-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), 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^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 ,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 a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

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.

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