1.Cho a,b,c >0. a+b+c=3.CMR:
a + ab + 2abc $\leq \frac{9}{2}$
2. Cho x,y,z>0. thỏa mãn: x(x + y + z) = 3yz.CMR:
$(x+y)^{3} + (x+z)^{3} + 3(x+y)(y+z)(z+x)\leq 5(y+z)^{3}$
02-04-2016 - 22:34
1.Cho a,b,c >0. a+b+c=3.CMR:
a + ab + 2abc $\leq \frac{9}{2}$
2. Cho x,y,z>0. thỏa mãn: x(x + y + z) = 3yz.CMR:
$(x+y)^{3} + (x+z)^{3} + 3(x+y)(y+z)(z+x)\leq 5(y+z)^{3}$
24-03-2016 - 14:55
Cho dãy số ( $x_{n}$) xác định như sau:
$\left\{\begin{matrix}x_{1}= \sqrt{30} & & & & \\ x_{n+1}= \sqrt{30x^{2}_ {n} +3x_{n} +2011} & & & \end{matrix}\right.$ $\forall n\notin N*$
Tìm lim$\frac{x_{n+1}}{x_{n}}$
24-03-2016 - 14:23
Cho x,y,z>0. CMR:
P= $\frac{2xy}{(z+x)(z+y)} + \frac{2yz}{(x+y)(x+z)} + \frac{3zx}{(y+z)(y+x)} \geq \frac{5}{3}$
20-01-2016 - 19:55
Cho x,y,z là các số thực dương, x + y + z = 3 , a $\geq$ 1. CMR
$\frac{1}{a^{x}}+\frac{1}{a^{y}}+\frac{1}{a^{z}} \geq \frac{x}{a^{x}} +\frac{y}{a^{y}}+\frac{z}{a^{z}}$
20-11-2015 - 19:48
1) $sin^{8}x +cos^{8}x=2(sin^{10}x + cos^{10}x)$ + $\frac{5}{4}cos2x$
2) $cos^{7}x+sin^{4}x=1$
3) $2sin3x - sin4x - cot^{2}x=3$
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