Câu 1:
\(A=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}=2\sqrt{2}\)
Câu 2:
\(\Leftrightarrow\left|2x-3\right|=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}=2\sqrt{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=2\sqrt{3}\\2x-3=-2\sqrt{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2\sqrt{3}+3}{2}\\x=\dfrac{-2\sqrt{3}+3}{2}\end{matrix}\right.\)
`1)A=\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}`
`A=\sqrt{3+2\sqrt{3}.\sqrt{2}+2}-\sqrt{3-2\sqrt{3}.\sqrt{2}+2}`
`A=\sqrt{(\sqrt{3}+\sqrt{2})^2}-\sqrt{(\sqrt{3}-\sqrt{2})^2}`
`A=|\sqrt{3}+\sqrt{2}|-|\sqrt{3}-\sqrt{2}|`
`A=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}=2\sqrt{2}`
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`2)\sqrt{4x^2-12x+9}=\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}`
`<=>\sqrt{4x^2-12x+9}=2\sqrt{2}` (Như câu `1`)
`<=>4x^2-12x+9=8`
`<=>4x^2-12x+1=0`
Ptr có:`\Delta'=(-6)^2-4=32 > 0`
`=>` Ptr có `2` nghiệm pb
`x_1=[-b+\sqrt{\Delta'}]/a=[-(-6)+\sqrt{32}]/4=[3+2\sqrt{2}]/2`
`x_2=[-b-\sqrt{\Delta'}]/a=[-(-6)-\sqrt{32}]/4=[3-2\sqrt{2}]/2`
Vậy `S={[3+-2\sqrt{2}]/2}`
