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killua0108

killua0108

Đăng ký: 28-08-2016
Offline Đăng nhập: 31-10-2016 - 17:49
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#651672 bpt $\sqrt{2x^{2}-2x+1}+\sqrt{2x^...

Gửi bởi killua0108 trong 28-08-2016 - 18:35

$\sqrt{2x^{2}-2x+1}+\sqrt{2x^{2}-(\sqrt{3}-1)x+1}+\sqrt{2x^{2}+(\sqrt{3}+1)x+1}\leq 3$

 

 

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bpt\Leftrightarrow  \sqrt{x^2+(x-1)^2)}+\sqrt{\frac{2+\sqrt{3}}{2}x^2+(\frac{\sqrt{3}-1}{2}x-1)^2}+\sqrt{\frac{2-\sqrt{3}}{2}x^2+(\frac{\sqrt{3}+1}{2}x+1)^2}\leq 3
 \leftrightarrow  do  x^2\geq 0\Rightarrow \left | x-1 \right | +\left | \frac{\sqrt{3}-1}{2}x-1 \right |+\left | \frac{\sqrt{3}+1}{2}x+1 \right |\leq 3
\Rightarrow \left | x-1+\frac{\sqrt{3}-1}{2}x-1+-\frac{\sqrt{3}+1}{2}x-1 \right |\leq 3
\Rightarrow 3\leq 3
nen.bpt.co.nghiem\Leftrightarrow x^2=0\Leftrightarrow x=0