Đáp án + Giải thích các bước giải:
`a.`
`M=(2sqrtx-9)/(x-5sqrtx+6)-(sqrtx+3)/(sqrtx-2)-(2sqrtx+1)/(3-sqrtx)` với `(x>0,xne4,xne9)`
`=(2sqrtx-9)/((sqrtx-2)(sqrtx-3))-(sqrtx+3)/(sqrtx-2)+(2sqrtx+1)/(sqrtx-3)`
`=(2sqrtx-9-(sqrtx+3)(sqrtx-3)+(2sqrtx+1)(sqrtx-2))/((sqrtx-2)(sqrtx-3))`
`=(2sqrtx-9-x+9+2x-4sqrtx+sqrtx-2)/((sqrtx-2)(sqrtx-3))`
`=(x-sqrtx-2)/((sqrtx-2)(sqrtx-3))`
`=((sqrtx-2)(sqrtx+1))/((sqrtx-2)(sqrtx-3))`
`=(sqrtx+1)/(sqrtx-3)`
`b.`
Ta có: `x=11-6sqrt2=9-6sqrt2+2=(3-sqrt2)^2`
Thay `x=(3-sqrt2)^2` vào biểu thức `M` ta được:
`M=\frac{sqrt((3-sqrt2)^2)+1}{sqrt((3-sqrt2)^2)-3}=\frac{3-sqrt2+1}{3-sqrt2-3}=-\frac{4-sqrt2}{sqrt2}=1-2sqrt2`
`c.`
Để `M=2`
`<=>(sqrtx+1)/(sqrtx-3)=2`
`<=>sqrtx+1=2(sqrtx-3)`
`<=>sqrtx+1=2sqrtx-6`
`<=>sqrtx=7`
`<=>x=49(TM)`
Vậy với `x=49` thì `M=2`
