Nếu $a,\,b,\,c,\,d > 0$ thỏa $ac+ bd= 2$ thì:
$$\frac{16}{a^{2}+ b^{2}+ c^{2}+ d^{2}}\leqq \sum\limits_{sym}\frac{1}{a}$$
$$\sum\limits_{cyc}\frac{a\left ( b+ c \right )}{a^{2}+ bc} \leqq \sum\limits_{sym}\frac{1}{a}$$
$$\frac{16}{a^{2}+ b^{2}+ c^{2}+ d^{2}} \leqq \sum\limits_{cyc}\frac{a\left ( b+ c \right )}{a^{2}+ bc} \,?$$