Đáp án:
`a)A=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}(x>=2)`
`<=>A^2=x+2\sqrt{x-1}+x-2\sqrt{x-1}+2\sqrt{(x+2\sqrt{x-1})(x-2\sqrt{x-1})}`
`<=>A^2=2x+2\sqrt{x^2-4(x-1)}`
`<=>A^2=2x+2\sqrt{x^2-4x+4}``
`<=>A^2=2x+2\sqrt{(x-2)^2}`
`<=>A^2=2x+2|x-2|`
`<=>A^2=2x+2(x-2)(do \ x>=2)`
`<=>A^2=4x-4=4(x-1)`
`<=>A=2\sqrt{x-1}(do \ A>=0)`
`b)B=\sqrt{x-2+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}}(x>=3)`
`<=>B^2=x-2+2\sqrt{x-3}+x+6+6\sqrt{x-3}+2\sqrt{(x-2+2\sqrt{x-3})(x+6+6\sqrt{x-3})}`
`<=>B^2=2x+4+8\sqrt{x-3}+2\sqrt{(\sqrt{x-3}+1)^2)(\sqrt{x-3}+3)^2}`
`<=>B^2=x-2+2\sqrt{x-3}+x+6+6\sqrt{x-3}+2|(\sqrt{x-3}+1)(\sqrt{x-3}+3)|`
`<=>B^2=(\sqrt{x-3}+1+\sqrt{x-3}+3)^2`
`<=>B=2\sqrt{x-3}+4.`
