$0< b\leqq a,\,\frac{b^{2}}{a}\leqq c\leqq \sqrt{ab}$. Chứng minh rằng:
$$\frac{a^{2}b^{2}}{a^{3}c+ b^{3}c}+ \frac{b^{2}c^{2}}{b^{3}a+ c^{3}a}+ \frac{c^{2}a^{2}}{c^{3}b+ a^{3}b}\leqq \frac{3}{2}$$
$0< b\leqq a,\,\frac{b^{2}}{a}\leqq c\leqq \sqrt{ab}$. Chứng minh rằng:
$$\frac{a^{2}b^{2}}{a^{3}c+ b^{3}c}+ \frac{b^{2}c^{2}}{b^{3}a+ c^{3}a}+ \frac{c^{2}a^{2}}{c^{3}b+ a^{3}b}\leqq \frac{3}{2}$$
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