Problem 1.
For all positive real numbers
,
prove that
Solution 1
Solution 2
Solution 3
Solution 1.
Solution 1
Solution 2.
Solution 2
Solution 3.
Solution 3
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,![\[
\frac{(a^2 + bc)^2}{b + c} + \frac{(b^2 + ca)^2}{c + a} + \frac{(c^2 + ab)^2}{a + b} \geq \frac{2abc(a + b + c)^2}{ab + bc + ca}.
\]](//latex.artofproblemsolving.com/e/7/0/e70d68c260be93ad221f67dbaa3adfd2b121a312.png)
,![\[
\frac{(a^2 + bc)^2}{b + c} + \frac{(b^2 + ca)^2}{c + a} + \frac{(c^2 + ab)^2}{a + b} \geq \frac{2abc(a + b + c)^2}{ab + bc + ca}.
\]](http://latex.artofproblemsolving.com/e/7/0/e70d68c260be93ad221f67dbaa3adfd2b121a312.png)