Ai giúp mình với ạ x – 2 $\sqrt{x-1}$ = 4 27/07/2021 Bởi Aubrey Ai giúp mình với ạ x – 2 $\sqrt{x-1}$ = 4
`x-2\sqrt{x-1}=4` (ĐKXĐ: `x>=4`) `<=> x-1-2\sqrt{x-1}+1=4` `<=> (\sqrt{x-1}-1)^2=4` `<=>`\(\left[ \begin{array}{l}\sqrt{x-1}-1=2\\\sqrt{x-1}-1=-2\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}\sqrt{x-1}=3\\\sqrt{x-1}=-1 (l)\end{array} \right.\) `=> x-1=9` `<=> x=10 ™` Vậy pt có tập nghiệm `S={10}` Bình luận
$x-2\sqrt[]{x-1}=4$ `<=>-2`$\sqrt[]{x-1}$`=4-x` `đkxđ:x>=4` `<=> (-2`$\sqrt[]{x-1})$$^{2}$ `=(4-x)^2` `<=>4(x-1)=16-8x+x^2` `<=>4x-4-16+8x-x^2=0` `<=>x^2-12x+20=0` `<=>(x-10)(x-2)=0` `<=>`\(\left[ \begin{array}{l}x-10=0\\x-2=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=10(tm)\\x=2(loại)\end{array} \right.\) vậy `x=10` Bình luận
`x-2\sqrt{x-1}=4` (ĐKXĐ: `x>=4`)
`<=> x-1-2\sqrt{x-1}+1=4`
`<=> (\sqrt{x-1}-1)^2=4`
`<=>`\(\left[ \begin{array}{l}\sqrt{x-1}-1=2\\\sqrt{x-1}-1=-2\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}\sqrt{x-1}=3\\\sqrt{x-1}=-1 (l)\end{array} \right.\)
`=> x-1=9`
`<=> x=10 ™`
Vậy pt có tập nghiệm `S={10}`
$x-2\sqrt[]{x-1}=4$
`<=>-2`$\sqrt[]{x-1}$`=4-x`
`đkxđ:x>=4`
`<=> (-2`$\sqrt[]{x-1})$$^{2}$ `=(4-x)^2`
`<=>4(x-1)=16-8x+x^2`
`<=>4x-4-16+8x-x^2=0`
`<=>x^2-12x+20=0`
`<=>(x-10)(x-2)=0`
`<=>`\(\left[ \begin{array}{l}x-10=0\\x-2=0\end{array} \right.\)`<=>` \(\left[ \begin{array}{l}x=10(tm)\\x=2(loại)\end{array} \right.\)
vậy `x=10`