\(\sqrt{4u-20}+3\sqrt{\dfrac{u-5}{9}}-\dfrac{1}{3}\sqrt{9u-45}=4\)
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AH
Akai Haruma
Giáo viên
15 tháng 10 2023
Lời giải:
a. ĐKXĐ: $x\geq 5$
PT $\Leftrightarrow \sqrt{4}.\sqrt{x-5}+\sqrt{x-5}=4+3.\sqrt{\frac{1}{9}}.\sqrt{x-5}$
$\Leftrightarrow 2\sqrt{x-5}+\sqrt{x-5}=4+\sqrt{x-5}$
$\Leftrightarrow 2\sqrt{x-5}=4$
$\Leftrightarrow \sqrt{x-5}=2$
$\Leftrightarrow x-5=4$
$\Leftrightarrow x=9$ (tm)
b. Sửa đoạn 4x-45 thành 4x-20.
ĐKXĐ: $x\geq 5$
PT $\Leftrightarrow \sqrt{4}.\sqrt{x-5}+\sqrt{\frac{1}{9}}.\sqrt{x-5}-\frac{1}{3}\sqrt{4}.\sqrt{x-5}=4$
$\Leftrightarrow 2\sqrt{x-5}+\frac{1}{3}\sqrt{x-5}-\frac{2}{3}\sqrt{x-5}=4$
$\Leftrightarrow \frac{5}{3}\sqrt{x-5}=4$
$\Leftrightarrow \sqrt{x-5}=\frac{12}{5}$
$\Leftrightarrow x-5=\frac{144}{25}=5,76$
$\Leftrightarrow x=10,76$ (tm)
MD
1
Y
4 tháng 8 2023
\(\dfrac{2}{3}\sqrt{9u-9}-\dfrac{1}{4}\sqrt{16u-16}+27\sqrt{\dfrac{u-1}{81}}=4\left(dk:u\ge1\right)\)
\(\Leftrightarrow\dfrac{2}{3}\sqrt{9\left(u-1\right)}-\dfrac{1}{4}\sqrt{16\left(u-1\right)}+27\dfrac{\sqrt{u-1}}{\sqrt{81}}=4\)
\(\Leftrightarrow2\sqrt{u-1}-\sqrt{u-1}+3\sqrt{u-1}=4\\ \Leftrightarrow\sqrt{u-1}.\left(2-1+3\right)=4\\ \Leftrightarrow4\sqrt{u-1}=4\\ \Leftrightarrow\sqrt{u-1}=1\\ \Leftrightarrow u-1=1\\ \Leftrightarrow u=2\left(tm\right)\)
Vậy \(S=\left\{2\right\}\)
22 tháng 7 2023
\(a) \sqrt{4x^2− 9} = 2\sqrt{x + 3}\)
\(ĐK:x\ge\dfrac{3}{2}\)
\(pt\Leftrightarrow4x^2-9=4\left(x+3\right)\)
\(\Leftrightarrow4x^2-9=4x+12\)
\(\Leftrightarrow4x^2-4x-21=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1-\sqrt{22}}{2}\left(l\right)\\x=\dfrac{1+\sqrt{22}}{2}\left(tm\right)\end{matrix}\right.\)
\(b)\sqrt{4x-20}+3.\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
\(ĐK:x\ge5\)
\(pt\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)
\(\Leftrightarrow2\sqrt{x-5}=4\Leftrightarrow\sqrt{x-5}=2\)
\(\Leftrightarrow x-5=4\Leftrightarrow x=9\left(tm\right)\)
22 tháng 7 2023
\(c)\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27.\sqrt{\dfrac{x-1}{81}}=4\)
ĐK:x>=1
\(pt\Leftrightarrow2\sqrt{x-1}-\sqrt{x-1}+3\sqrt{x-1}=4\)
\(\Leftrightarrow4\sqrt{x-1}=4\Leftrightarrow\sqrt{x-1}=1\)
\(\Leftrightarrow x-1=1\Leftrightarrow x=2\left(tm\right)\)
\(d)5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)
\(ĐK:x\ge3\)
\(pt\Leftrightarrow3\sqrt{x-3}-\dfrac{14}{3}\sqrt{x-3}-7\sqrt{x^2-9}+6\sqrt{x^2-9}=0\)
\(\Leftrightarrow-\dfrac{5}{3}\sqrt{x-3}-\sqrt{x^2-9}=0\Leftrightarrow\dfrac{5}{3}\sqrt{x-3}+\sqrt{x^2-9}=0\)
\(\Leftrightarrow(\dfrac{5}{3}+\sqrt{x+3})\sqrt{x-3}=0\)
\(\Leftrightarrow\sqrt{x-3}=0\) (vì \(\dfrac{5}{3}+\sqrt{x+3}>0\))
\(\Leftrightarrow x-3=0\Leftrightarrow x=3\left(nhận\right)\)
HN
3
23 tháng 6 2021
\(\dfrac{1}{3}\sqrt{45}-\sqrt{20}+\sqrt{9+4\sqrt{5}}\)
= \(\dfrac{1}{3}.3.\sqrt{5}-2\sqrt{5}+\sqrt{\left(2+\sqrt{5}\right)^2}\)
= \(\sqrt{5}-2\sqrt{5}+2+\sqrt{5}=2\)
AT
23 tháng 6 2021
\(\dfrac{1}{3}\sqrt{45}-\sqrt{20}+\sqrt{9+4\sqrt{5}}=\dfrac{1}{3}\sqrt{9.5}-\sqrt{4.5}+\sqrt{2^2+2.2.\sqrt{5}+\left(\sqrt{5}\right)^2}\)
\(\dfrac{1}{3}.3\sqrt{5}-2\sqrt{5}+\sqrt{\left(2+\sqrt{5}\right)^2}=\sqrt{5}-2\sqrt{5}+\left|2+\sqrt{5}\right|\)
\(=\sqrt{5}-2\sqrt{5}+2+\sqrt{5}=2\)
HT
1
HP
29 tháng 8 2021
9.
\(\sqrt{20}+2\sqrt{45}+\sqrt{125}-3\sqrt{80}\)
\(=2\sqrt{5}+6\sqrt{5}+5\sqrt{5}-12\sqrt{5}\)
\(=-\sqrt{5}\)
HP
29 tháng 8 2021
10.
\(\sqrt{75}-\sqrt{5\dfrac{1}{3}}+\dfrac{9}{2}\sqrt{2\dfrac{2}{3}}+2\sqrt{27}\)
\(=5\sqrt{3}-\sqrt{5+\dfrac{1}{3}}+\dfrac{9}{2}\sqrt{2+\dfrac{2}{3}}+6\sqrt{3}\)
\(=11\sqrt{3}-\sqrt{\dfrac{16}{3}}+\dfrac{9}{2}\sqrt{\dfrac{8}{3}}\)
\(=11\sqrt{3}-\dfrac{4\sqrt{3}}{3}+3\sqrt{6}\)
\(=\dfrac{29\sqrt{3}}{3}+3\sqrt{6}\)
15 tháng 9 2017
1,
a,\(4\sqrt{\dfrac{9}{2}}+\sqrt{2}+\sqrt{\dfrac{1}{18}}=4\sqrt{\dfrac{18}{4}}+\sqrt{2}+\sqrt{\dfrac{1}{9.2}}=4\dfrac{\sqrt{18}}{2}+\sqrt{2}+\dfrac{1}{3}\sqrt{\dfrac{1}{2}}=2\sqrt{9.2}+\sqrt{2}+\dfrac{1}{3}\sqrt{\dfrac{2}{4}}=2.3\sqrt{2}+\sqrt{2}+\dfrac{\sqrt{2}}{6}=6\sqrt{2}+\sqrt{2}+\sqrt{2}\dfrac{1}{6}=\dfrac{43}{6}\sqrt{2}\) b,\(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}=4\sqrt{4.5}-3\sqrt{25.5}+5\sqrt{9.5}-15\dfrac{\sqrt{5}}{5}=4.2\sqrt{5}-3.5\sqrt{5}+5.3\sqrt{5}-3\sqrt{5}=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}=5\sqrt{5}\)
TD
15 tháng 9 2017
*) Giải phương trình :
\(\sqrt{4x-8}+5\sqrt{x-2}-\sqrt{9x-18}=20\) ( ĐKXĐ : x \(\ge\) 2 )
\(\Leftrightarrow\sqrt{4\left(x-2\right)}+5\sqrt{x-2}-\sqrt{9\left(x-2\right)}=20\)
\(\Leftrightarrow2\sqrt{x-2}+5\sqrt{x-2}-3\sqrt{x-2}=20\)
\(\Leftrightarrow4\sqrt{x-2}=20\)
\(\Leftrightarrow\sqrt{x-2}=5\)
\(\Leftrightarrow x-2=25\)
\(\Leftrightarrow x=27\) ( thỏa mãn điều kiện )
Vậy phương trình có nghiệm x = 27 .
MH
1
2 tháng 11 2021
a) \(pt\Leftrightarrow\sqrt{\left(x-3\right)^2}=3\Leftrightarrow\left|x-3\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=3\\x-3=-3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=0\end{matrix}\right.\)
b) ĐKXĐ: \(x\ge-5\)
\(pt\Leftrightarrow2\sqrt{x+5}+\sqrt{x+5}-\sqrt{x+5}=4\)
\(\Leftrightarrow2\sqrt{x+5}=4\Leftrightarrow\sqrt{x+5}=2\)
\(\Leftrightarrow x+5=4\Leftrightarrow x=-1\left(tm\right)\)
\(\sqrt{4u-20}+3\sqrt{\dfrac{u-5}{9}}-\dfrac{1}{3}\sqrt{9u-45}=4\) (ĐK: \(u\ge5\))
\(\Leftrightarrow2\sqrt{u-5}+3\cdot\dfrac{\sqrt{u-5}}{3}-\dfrac{1}{3}\cdot3\sqrt{u-5}=4\)
\(\Leftrightarrow2\sqrt{u-5}+\sqrt{u-5}-\sqrt{u-5}=4\)
\(\Leftrightarrow2\sqrt{u-5}=4\)
\(\Leftrightarrow\sqrt{u-5}=2\)
\(\Leftrightarrow u-5=4\)
\(\Leftrightarrow u=9\) (tm)