" If "a+(1)/(b)=1" and "b+(1)/(c)=1," then show that "c+(1)/(a)=1

If a^(2)/(b + c) = b^(2)/(c +a) = c^(2)/(a + b) = 1 , then show that 1/(1+a) + 1/(1 + b) + 1/(1+c) = 1 .

If a^2/(b+c)=b^2/(a+c)=c^2/(a+b)=1 , then show that 1/(1+a)+1/(1+b)+1/(1+c)=1 .

If (b+c)/(a), (c+a)/(b), (a+b)/(c ) are in A.P. show that (1)/(a), (1)/(b), (1)/(c ) are also in A.P. (a+b+c != 0) .

If x^(1/a)=y^(1/b)=z^(1/c)" and "xyz = 1 , then show that a+b+c=0 .

If (b+c)/(a),(c+a)/(b),(a+b)/(c) are in A.P. show that (1)/(a),(1)/(b)(1)/(c) are also in A.P.(a+b+c!=0)

If |(a,1,1),(1,b,1),(1,1,c)|=0 then show that 1/(1-a)+1/(1-b)+1/(1-c)=1

If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

If a ((1)/(b) + (1)/(c)) , b((1)/(c) + (1)/(a)) , c ((1)/(a)+ (1)/(b)) are in AP then a, b, c are in :

If a^2/(b+c)=b^2/(c+a)=c^2/(a+b)=1 , show that 1/(1+a)+1/(1+b)+1/(1+c)=1