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herolnq

herolnq

Đăng ký: 16-02-2013
Offline Đăng nhập: 08-02-2014 - 12:50
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$S=\frac{bc+a^2-b\sqrt{a^2+c^2}+c\sqrt{a^2+b^2...

06-02-2014 - 21:22

cho b>c. tìm max

$S=\frac{bc+a^2-b\sqrt{a^2+c^2}+c\sqrt{a^2+b^2}}{\sqrt{(a^2+b^2)(a^2+c^2)}}$


$(ax+by+cz)(\frac{a}{x}+\frac{b}{y...

06-02-2014 - 21:19

cho 0<a<b<c. CMR mọi x,y,z ta có

$(ax+by+cz)(\frac{a}{x}+\frac{b}{y}+\frac{c}{z})\leqslant \frac{(a+c)^2}{4ac}(x+y+z)^2$


$|(a^2-b^2)(b^2-c^2)(c^2-a^2)|\leqslant \sqrt{5}$

06-02-2014 - 21:13

cho a.b.c>= 0

a+b+c=$\sqrt{5}$

$|(a^2-b^2)(b^2-c^2)(c^2-a^2)|\leqslant \sqrt{5}$


$\left\{\begin{matrix} 2y^3-y^2(x+4)+8y+x^2-4x=0...

06-02-2014 - 20:54

$\left\{\begin{matrix} 2y^3-y^2(x+4)+8y+x^2-4x=0 & \\ \sqrt{\frac{11-x}{2}}+\sqrt{x+2y^3}=4(1-x)^2+8y-\frac{1}{2} & \end{matrix}\right.$


$(2\sqrt{2x-1}-4)x^2+(7-4\sqrt{2x-1})x+\sqrt...

06-02-2014 - 20:34

$(2\sqrt{2x-1}-4)x^2+(7-4\sqrt{2x-1})x+\sqrt{2x-1}-3=0$