Cho $a,b,c\geq 0$. Chứng minh rằng:
$\frac{3(a^{4}+b^{4}+c^{4})}{(a^{2}+b^{2}+c^{2})^{2}}+\frac{ab+bc+ca}{a^{2}+b^{2}+c^{2}}\geq 2$
Cho $a,b,c\geq 0$. Chứng minh rằng:
$\frac{3(a^{4}+b^{4}+c^{4})}{(a^{2}+b^{2}+c^{2})^{2}}+\frac{ab+bc+ca}{a^{2}+b^{2}+c^{2}}\geq 2$
Cho $a,b,c\geq 0$. Chứng minh rằng:
$\frac{3(a^{4}+b^{4}+c^{4})}{(a^{2}+b^{2}+c^{2})^{2}}+\frac{ab+bc+ca}{a^{2}+b^{2}+c^{2}}\geq 2$
Bởi vì
\[\frac{3(a^{4}+b^{4}+c^{4})}{(a^{2}+b^{2}+c^{2})^{2}}+\frac{ab+bc+ca}{a^{2}+b^{2}+c^{2}} - 2 = \frac{\displaystyle \sum (a-b)^2(a+b-c)^2 + 4 \sum ab(a-b)^2}{2(a^2+b^2+c^2)} \geqslant 0.\]
Edited by Nguyenhuyen_AG, 23-02-2017 - 00:10.
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