Đáp án+Giải thích các bước giải:
`a)P=\frac{x-3}{\sqrt{x-1}-\sqrt{2}}(x>=1,x\ne3)`
`=\frac{x-1-2}{\sqrt{x-1}-\sqrt{2}}`
`=\frac{(\sqrt{x-1})^2-\sqrt{2}^2}{\sqrt{x-1}-\sqrt{2]}`
`=\frac{(sqrt{x-1}-\sqrt{2})(\sqrt{x-1}+\sqrt{2})}{\sqrt{x-1]-\sqrt{2}}`
`=\sqrt{x-1}+\sqrt{2}`
`b)x=4(2-\sqrt{3})`
`=>P=\sqrt{4(2-\sqrt{3})-1}+\sqrt{2}`
`=\sqrt{8-4\sqrt{3}-1}+\sqrt{2}=\sqrt{7-4\sqrt{3}}+\sqrt{2}`
`=\sqrt{(2-\sqrt{3})^2}+\sqrt{2}=|2-\sqrt{3}|+\sqrt{2}`
`=2-\sqrt{3}+\sqrt{2}`
`=>x=4(2-\sqrt{3})<=>P=2-\sqrt{3}+\sqrt{2}`
`c)P=\sqrt{x-1}+\sqrt{2}`
Vì `\sqrt{x-1}>=0`
`=>\sqrt{x-1}+\sqrt{2}>=\sqrt{2}`
Dấu `=` xảy ra khi `\sqrt{x-1]=0<=>x-1=0<=>x=1`
Vậy `GTNNNN=\sqrt{2}` khi `x=1`
