Môn Toán Lớp 9 Mong mn giúp e hứa 5 sao ạ
Question
Sarah
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Trả lời ( )
Đáp án:
Giải thích các bước giải:
Đáp án + Giải thích các bước giải:
`a.`
`P=(sqrtx-1/sqrtx):((sqrtx-1)/sqrtx+(1-sqrtx)/(x+sqrtx))` `(x>0,xne1)`
`=(sqrtx-\frac{1}{sqrtx}):\frac{(sqrtx-1)(sqrtx+1)+1-sqrtx}{sqrtx(sqrtx+1)}`
`=\frac{x-1}{sqrtx}:\frac{x-1+1-sqrtx}{sqrtx(sqrtx+1)}`
`=\frac{x-1}{sqrtx}:\frac{x-sqrtx}{sqrtx(sqrtx+1)}`
`=\frac{x-1}{sqrtx}. \frac{sqrtx(sqrtx+1)}{x-sqrtx}`
`=\frac{(sqrtx-1)(sqrtx+1)}{sqrtx}. \frac{sqrtx(sqrtx+1)}{sqrtx(sqrtx-1)}`
`=\frac{(sqrtx+1)^2}{sqrtx}`
`b.`
Với `x=2/(2+sqrt3)=(2(2-sqrt3))/[(2+sqrt3)(2-sqrt3)]=4-2sqrt3`
Thay `x=4-2sqrt3` vào `P` ta được:
`P=\frac{(sqrt(4-2sqrt3)+1)^2}{sqrt(4-2sqrt3)}`
`=\frac{(sqrt(3-2sqrt3+1)+1)^2}{sqrt(3-2sqrt3+1)}`
`=\frac{(sqrt((sqrt3-1)^2)+1)^2}{sqrt((sqrt3-1)^2)}`
`=\frac{(sqrt3-1+1)^2}{sqrt3-1}`
`=\frac{3(sqrt3+1)}{(sqrt3-1)(sqrt3+1)}`
`=\frac{3sqrt3+3}{3-1}`
`=\frac{3sqrt3+3}{2}`