A geometric inequality?
Algebra
Level
4
\[{\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+x)(y+z)}+\frac{z^2}{(z+x)(z+y)}<A}\]
The above inequality is true for any positive numbers \(x, y,\) and \(z\). Find the smallest number \(A,\) and prove that your answer is right.
by
Arturo Presa