có P = 1+x + \frac{x^{2}}{1-x}+1+y + \frac{y^{2}}{1-y} + \frac{1}{x+y} -2 = \frac{1}{1-x} + \frac{1}{1-y} + \frac{1}{x+y} -2 có ((1-x)+(1-y)+(x+y)) ( \frac{1}{1-x} + \frac{1}{1-y} + \frac{1}{x+y} \geq 9 \Rightarrow \frac{1}{1-x} + \frac{1}{1-y} + \frac{1}{x+y} \geq \frac{9}{2} \Rightarrow P \geq \frac{5}{2} dấu "=" \Leftrightarrow x=y= \frac{1}{3}
có P = 1+x +
\frac{x^{2}}{1-x}+1+y +
\frac{y^{2}}{1-y} +
\frac{1}{x+y} -2 =
\frac{1}{1-x} +
\frac{1}{1-y} +
\frac{1}{x+y} -2 có ((1-x)+(1-y)+(x+y)) (
\frac{1}{1-x} +
\frac{1}{1-y} + $\frac{1}{x+y}
) \geq
9 \Rightarrow
\frac{1}{1-x}
+ \frac{1}{1-y}
+ \frac{1}{x+y}
\geq
\frac{9}{2}
\Rightarrow
P \geq
\frac{5}{2}
dấu "=" \Leftrightarrow
x=y= \frac{1}{3}$