Câu hỏi 76
Chứng minh rằng nếu $a,b,c\gt 0$ thì
$$\frac{a^2(a^3+b^3)}{a^2+ab+b^2}+\frac{b^2(b^3+c^3)}{b^2+bc+c^2}+\frac{c^2(c^3+a^3)}{c^2+ca+a^2}\ge2abc.$$
$$\frac{a^2(a^3+b^3)}{a^2+ab+b^2}+\frac{b^2(b^3+c^3)}{b^2+bc+c^2}+\frac{c^2(c^3+a^3)}{c^2+ca+a^2}\ge2abc.$$