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Giải thích các bước giải :
`sqrt(5+2sqrt6)-sqrt(5-2sqrt6)=sqrt(3+2sqrt3.sqrt2+2)-sqrt(3-2sqrt3.sqrt2+2)=sqrt((sqrt3+sqrt2)^2)-sqrt((sqrt3-sqrt2)^2)=|sqrt3+sqrt2|-|sqrt3-sqrt2|=sqrt3+sqrt2-sqrt3+sqrt2=2sqrt2=sqrt8<sqrt26`
Vậy : `sqrt(5+2sqrt6)-sqrt(5-2sqrt6)<sqrt26`
`\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}`
`=\sqrt{(\sqrt{3})^2+2.\sqrt{3}.\sqrt{2}+(\sqrt{2})^2}-\sqrt{(\sqrt{3})^2-2.\sqrt{3}.\sqrt{2}+(\sqrt{2})^2}`
`=\sqrt{(\sqrt{3}+\sqrt{2})^2}-\sqrt{(\sqrt{3}-\sqrt{2})^2}`
`=|\sqrt{3}+\sqrt{2}|-|\sqrt{3}-\sqrt{2}|`
`=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}`
`=2\sqrt{2}`
`=\sqrt{8}`
Vì `\sqrt{8}<\sqrt{26}` nên `\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}<\sqrt{26}`
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