Cho $a,b,c\geq 0, a+b+c=1$ CMR:
$\sqrt{a+\frac{(b-c)^{2}}{4}} +\sqrt{b}+\sqrt{c}\leq \sqrt{3}$
28-08-2017 - 23:26
Cho $a,b,c\geq 0, a+b+c=1$ CMR:
$\sqrt{a+\frac{(b-c)^{2}}{4}} +\sqrt{b}+\sqrt{c}\leq \sqrt{3}$
17-06-2017 - 22:54
Cho $x, y, z > 0, x+y+z=xyz$
Tìm max $P=\frac{x}{x^{2}+1}+\frac{y}{y^{2}+1}+\frac{z}{z^{2}+1}$
19-05-2017 - 22:13
Cho $\ P(x)$, $degP=n$, hệ số cao nhất là $\ a$, $\sqrt{1-x^{2}}\left | P(x)\right |\leq1 \forall x\in \left [ -1;1 \right ]$
CMR: $\left | a \right |\leq 2^{n}$
06-01-2017 - 10:24
Cho $a,b,c \in \left [ 0;1 \right ]$
Chưng minh rằng $a^{2}+b^{2}+c^{2}\leq a^{2}b+b^{2}c+c^{2}a+1$
09-11-2016 - 22:59
Cho $x,y,z > 0$. Chứng minh rằng
$\frac{x^{2}y}{z}+\frac{y^{2}z}{x}+\frac{z^{2}x}{y}\geq x^{2}+y^{2}+z^{2}$
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