BPT vô tỉ

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+$Bpt$ \Leftrightarrow $2(x-1)+(x-1)\sqrt{(x-1)^{2}+4}$ \geq $2(2x)+(2x)\sqrt{(2x)^{2}+4}$


\Leftrightarrow $x-1$ \geq $2x$ \Leftrightarrow $x$ \leq $-1$ vì $f(t)=2t+t\sqrt{t^{2}+4}$: luôn tăng
 
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