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TD
20 tháng 9 2017
a) \(\sqrt{25x+75}+3\sqrt{x-2}=2+4\sqrt{x+3}+\sqrt{9x-18}\) (ĐKXĐ : \(x\ge2\) )
\(\Leftrightarrow5\sqrt{x+3}+3\sqrt{x-2}-4\sqrt{x+3}-3\sqrt{x-2}=2\)
\(\Leftrightarrow\sqrt{x+3}=2\)
\(\Leftrightarrow x+3=4\)
\(\Leftrightarrow x=1\) ( Thỏa mãn ĐKXĐ )
TD
20 tháng 9 2017
c) \(\sqrt{4x+20}+\sqrt{x+5}-\dfrac{1}{3}\sqrt{9x+45}=4\) (ĐKXĐ : \(x\ge-5\) )
\(\Leftrightarrow2\sqrt{x+5}+\sqrt{x+5}-\sqrt{x+5}=4\)
\(\Leftrightarrow2\sqrt{x+5}=4\)
\(\Leftrightarrow\sqrt{x+5}=2\)
\(\Leftrightarrow x+5=4\)
\(\Leftrightarrow x=-1\) ( Thỏa mãn ĐKXĐ )
Vậy.......
19 tháng 8 2016
a/ \(\sqrt{x-1}+\sqrt{4x-4}-\sqrt{25x-25}+2=0\) (ĐKXĐ : \(x\ge1\))
\(\Leftrightarrow\sqrt{x-1}+2\sqrt{x-1}-5\sqrt{x-1}+2=0\)
\(\Leftrightarrow2\sqrt{x-1}=2\Leftrightarrow x-1=1\Leftrightarrow x=2\)
b/ \(\sqrt{9x^2+18}+2\sqrt{x^2+2}-\sqrt{25x^2+50}+3=0\)
\(\Leftrightarrow3\sqrt{x^2+2}+2\sqrt{x^2+2}-5\sqrt{x^2+2}+3=0\)
<=> 3 = 0 (vô lý)
=> pt vô nghiệm.
19 tháng 8 2016
c/ \(\frac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\) (ĐKXĐ : x>-5/7)
\(\Leftrightarrow9x-7=7x+5\Leftrightarrow2x=12\Leftrightarrow x=6\)
d/ \(\frac{\sqrt{2x-3}}{\sqrt{x-1}}=2\) (ĐKXĐ : \(x\ge\frac{3}{2}\))
\(\Leftrightarrow2x-3=4\left(x-1\Leftrightarrow\right)2x=1\Leftrightarrow x=\frac{1}{2}\) (loại)
Vậy pt vô nghiệm.
NA
9 tháng 10 2018
\(\sqrt{16x-32}+\sqrt{25x-50}=187\sqrt{9x-18}\)
\(\Leftrightarrow\sqrt{16\left(x-2\right)}+\sqrt{25\left(x-2\right)}=187\sqrt{9\left(x-2\right)}\)
\(\Leftrightarrow4\sqrt{x-2}+5\sqrt{x-2}=561\sqrt{x-2}\)
\(\Leftrightarrow552\sqrt{x-2}=0\)
\(\Leftrightarrow\sqrt{x-2}=0\)
\(\Leftrightarrow x-2=0\Leftrightarrow x=2\)
TN
0
29 tháng 7 2017
ĐK: \(x\ge -2\)
\(\sqrt{9x+18}-5\sqrt{x+2}+\dfrac{4}{5}\sqrt{25x+50}=6\)
\(pt\Leftrightarrow\left(\sqrt{9x+18}-9\right)-\left(5\sqrt{x+2}-15\right)+\left(\dfrac{4}{5}\sqrt{25x+50}-12\right)=0\)
\(\Leftrightarrow\dfrac{9x+18-81}{\sqrt{9x+18}+9}-\dfrac{25\left(x+2\right)-225}{5\sqrt{x+2}+15}+\dfrac{\dfrac{16}{25}\left(25x+50\right)-144}{\dfrac{4}{5}\sqrt{25x+50}+12}=0\)
\(\Leftrightarrow\dfrac{9x-63}{\sqrt{9x+18}+9}-\dfrac{25x-175}{5\sqrt{x+2}+15}+\dfrac{16x-112}{\dfrac{4}{5}\sqrt{25x+50}+12}=0\)
\(\Leftrightarrow\dfrac{9\left(x-7\right)}{\sqrt{9x+18}+9}-\dfrac{25\left(x-7\right)}{5\sqrt{x+2}+15}+\dfrac{16\left(x-7\right)}{\dfrac{4}{5}\sqrt{25x+50}+12}=0\)
\(\Leftrightarrow\left(x-7\right)\left(\dfrac{9}{\sqrt{9x+18}+9}-\dfrac{25}{5\sqrt{x+2}+15}+\dfrac{16}{\dfrac{4}{5}\sqrt{25x+50}+12}\right)=0\)
Dễ thấy: \(\dfrac{9}{\sqrt{9x+18}+9}-\dfrac{25}{5\sqrt{x+2}+15}+\dfrac{16}{\dfrac{4}{5}\sqrt{25x+50}+12}>0\forall x\ge-2\)
\(\Rightarrow x-7=0\Rightarrow x=7\)
27 tháng 8 2022
a: \(=2\sqrt{x-3}+3\sqrt{x-3}-4\sqrt{x-3}+3-x\)
\(=\sqrt{x-3}+3-x\)
c: \(\Leftrightarrow7\sqrt{x-2}-2\sqrt{x-2}-3\sqrt{x-2}=18\)
=>2 căn x-2=18
=>x-2=81
=>x=83
DS
1
28 tháng 9 2019
2) \(\frac{1}{5}\sqrt{25x+50}-5\sqrt{x+2}+\sqrt{9x+18}+9=0\)
\(\frac{1}{5}\sqrt{25\left(x+2\right)}-5\sqrt{x+2}+\sqrt{9x+18}+9=0\)
\(\frac{1}{5}.\sqrt{25}.\sqrt{x+2}-5\sqrt{x+2}+\sqrt{9x+18}+9=0\)
\(\frac{1}{5}.5\sqrt{x+2}-5\sqrt{x+2}+\sqrt{9x+18}+9=0\)
\(\frac{1}{5}.5\sqrt{x+2}-5\sqrt{x+2}+\sqrt{9\left(x+2\right)}+9=0\)
\(\frac{1}{5}.5\sqrt{x+2}-5\sqrt{x+2}+\sqrt{9}.\sqrt{x+2}+9=0\)
\(\frac{1}{5}.5\sqrt{x+2}-5\sqrt{x+2}+3\sqrt{x+2}+9=0\)
\(\sqrt{x+2}-5\sqrt{x+2}+3\sqrt{x+2}+9=0\)
\(-\sqrt{x+2}=-9\)
\(x+2=81\)
\(\Rightarrow x=79\)
3) \(\sqrt{x^2-4x+4}=7x-1\)
\(\sqrt{x^2-2.x.2+2^2}=7x-1\)
\(\sqrt{\left(x-2\right)^2}=7x-1\)
\(x-2=7x-1\)
\(-2=7x-1-x\)
\(-2+1=7x-x\)
\(-1=6x\)
\(-\frac{1}{6}=x\)
\(\Rightarrow x=-\frac{1}{6}\)
6 tháng 10 2017
\(\sqrt{25x+75}+3\sqrt{x-2}-2+4\sqrt{x+3}\)\(+\sqrt{9x-18}\)
= \(5\sqrt{x+3}+3\sqrt{x-2}-2+4\sqrt{x+3}+3\sqrt{x-2}\)
= \(9\sqrt{x+3}+6\sqrt{x-2}-2\)
N
9 tháng 10 2019
a.
\(DK:49-28x-4x^2\ge0\)
PT\(\Leftrightarrow\sqrt{49-28x-4x^2}=5\)
\(\Leftrightarrow49-28x-4x^2=25\)
\(\Leftrightarrow4x^2+28x-24=0\)
\(\Leftrightarrow x^2+7x-6=0\)
Ta co:
\(\Delta=7^2-4.1.\left(-6\right)=73>0\)
\(\Rightarrow\hept{\begin{cases}x_1=\frac{-7+\sqrt{73}}{2}\left(n\right)\\x_2=\frac{-7-\sqrt{73}}{2}\left(n\right)\end{cases}}\)
Vay nghiem cua PT la \(\hept{\begin{cases}x_1=\frac{-7+\sqrt{73}}{2}\\x_2=\frac{-7-\sqrt{73}}{2}\end{cases}}\)
\(\sqrt{25x-5-\sqrt{9x-18}}=8\)
\(\Rightarrow25x-\sqrt{9x-18}=69\)
\(\Rightarrow9x-18=4761-3450x+\left(25x\right)^2\)
\(\Rightarrow-\left(25x\right)^2+3459x-4779=0\)
\(\Rightarrow\left(25x\right)^2-3459x+4779=0\)
\(\Rightarrow\left(25x-69,18\right)^2=6,8724\)
Làm nốt