- #1
topengonzo
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Homework Statement
How to prove (a+1/a)^2 + (b+1/b)^2 >= 25/2 given that a+b=1 and a,b positive
Homework Equations
The Attempt at a Solution
I tried replacing b with 1-a but I get 6th degree a which I don't know how to find inequality for.
Since a and b are perfect symmetric in this problem then a=b=0.5 is of interest. I get that its the minimum.
I tried Lagrange multiplier but I get an equation with 3rd degree. By trial and error, I got solution.
Is there any other way of finding solution? By expanding it?