FYR Macedonia

[egal]

Don't understand the solution. What is "AH mean inequality", arithmetic-harmonic mean? In that case I don't get the same inequality

 

[lex]

[imath]\dfrac{x_1+x_2+x_3}{3}≥\dfrac{3}{\tfrac{1}{x_1}+\tfrac{1}{x_2}+\tfrac{1}{x_3}}[/imath]
[imath]x_1=\dfrac{ab}{a+b}, \,x_2=\dfrac{bc}{b+c},\, x_3=\dfrac{ca}{c+a}[/imath]

and it should work out. If not, post your work and we can have a look.

 

[egal]

[imath]\dfrac{x_1+x_2+x_3}{3}≥\dfrac{3}{\tfrac{1}{x_1}+\tfrac{1}{x_2}+\tfrac{1}{x_3}}[/imath]
[imath]x_1=\dfrac{ab}{a+b}, \,x_2=\dfrac{bc}{b+c},\, x_3=\dfrac{ca}{c+a}[/imath]

and it should work out. If not, post your work and we can have a look.

Thank you, I got it now.