giup minh bài 20 câu d với bài 22 với .
22.
[tex]\dpi{100} \sqrt{(n+1)^2}+\sqrt{n^2}=|n+1|+|n|=n+1+n=2n+1(1)\\(n+1)^2-n^2=(n+1+n)(n+1-n)=(2n+1).1=2n+1(2)\\\(1)va(2)Rightarrow \sqrt{(n+1)^2}+\sqrt{n^2}=(n+1)^2-n^2[/tex]
20d
[tex]\dpi{100} (\sqrt{11}-\sqrt{3})^2=11-2\sqrt{33}+3=14-2\sqrt{33}=14-\sqrt{132}\\2^2=4=14-10=14-\sqrt{100}\\\sqrt{132}>\sqrt{100}\Rightarrow -\sqrt{132}<-\sqrt{100}\Rightarrow 14-\sqrt{132}<14-\sqrt{100}\Leftrightarrow (\sqrt{11}-\sqrt{3})^2<2^2\\(\sqrt{11}-\sqrt{3})^2<2^2\\\Leftrightarrow \sqrt{(\sqrt{11}-\sqrt{3})^2}<\sqrt{2^2}\\\Leftrightarrow \sqrt{11}-\sqrt{3}<2[/tex]
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