[Thgx0312555]

เพิ่มตัวอย่างโจทย์(ไม่ยาก)ด้วยนะครับ
1. Let $a,b,c$ be positive real numbers such that $a+b+c=1$
Prove that
$$\Big(\sqrt{a^4+b^4+c^4}\Big)\left(\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{a+b}\right) \ge \frac{1}{\sqrt{2}}$$
2. Let $a,b,c$ be positive real numbers such that $ab+bc+ca=3$
Prove that
$$\frac{1}{1+a^2(b+c)}+\frac{1}{1+b^2(c+a)}+\frac{1}{1+c^2(a+b)} \le \frac{1}{abc}$$
3. Let $a,b,c$ be positive real numbers such that $abc=1$ Prove that
$$\sum_{cyc} \frac{1}{a^2+2b^2+3} \le \frac{1}{2}$$