Giải các phương trình
a)5x-3=7
b)(x+3)(x-4)=0
c)/x\(^2\)+2014/=1
d)\(\dfrac{2}{x+1}-\dfrac{1}{x-3}=\dfrac{3x-11}{x^2-2x-3}\)
K
Khách
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Những câu hỏi liên quan
5 tháng 4 2021
|x-9|=2x+5
Xét 3 TH
TH1: x>9 => x-9=2x+5 =>-9-5=x =>x=-14 (L)
TH2: x<9 => 9-x=2x+5 => 9-5=3x =>x=4/3(t/m)
TH3: x=9 =>0=23(L)
Vậy x= 4/3
5 tháng 4 2021
Ta có:\(\dfrac{1-2x}{4}-2\le\dfrac{1-5x}{8}+x\\ \)
\(\dfrac{2-4x-16}{8}\le\dfrac{1-5x+8x}{8}\)
\(-4x-14\le1+3x\\ \Leftrightarrow7x+15\ge0\\ \Leftrightarrow x\ge-\dfrac{15}{7}\)
16 tháng 1 2019
2.a)\(\dfrac{3\text{x}-2}{2}\)=\(\dfrac{1-2\text{x}}{3}\)
<=>\(\dfrac{9\text{x}-6}{6}\)=\(\dfrac{2-4\text{x}}{6}\)
<=>9x-6=2-4x
<=>9x+4x=2+6
<=>13x=8
<=>x=\(\dfrac{8}{13}\)
16 tháng 1 2019
1.a)2(x-0,5)+3=0,25(4x-1)
<=>2x-1+3=x-1phần4
<=>2x-x=-1/4+1-3
<=>x=-3/4
KK
30 tháng 3 2022
a)\(\dfrac{7x-1}{2}+2x=\dfrac{16-x}{3}\)
\(\dfrac{\left(7x-1\right).3}{2.3}+\dfrac{2x.6}{6}=\dfrac{\left(16-x\right)2}{3.2}\)
khử mẫu
=> (7x-1).3+12x=(16-x).2
=>21x-3+12x=-2x+32
=>21x-3+12x+2x-32=0
=>35x-35=0
KK
30 tháng 3 2022
b)\(\dfrac{x+1}{x-2}+\dfrac{x-1}{x+2}=\dfrac{2\left(x^2+2\right)}{x^2-4}\)
ĐKXĐ: x khác +-2
\(\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{\left(x-1\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{2\left(x^2+2\right)}{\left(x-2\right)\left(x+2\right)}\)
khử mẫu
(x+1).(x+2)+(x-1)(x-2)=2x2+4
=>x2+x+2+x+2+x2-2x-x+2=2x2+4
=>x2+x+2+x+2+x2-2x-x+2-2x2-4=0
=>(x2+x2-2x2)+(x+x-2x-x)+(2+2+2-4)=0
=>-x+2=0
=>-x=-2
=>x=2(loại)
vậy pt vô nghiệm
AH
Akai Haruma
Giáo viên
1 tháng 10 2021
Lời giải:
a. ĐKXĐ: $x\geq 0$
$2\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}=28$
$\Leftrightarrow 2\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}=28$
$\Leftrightarrow 13\sqrt{2x}=28$
$\Leftrightarrow \sqrt{2x}=\frac{28}{13}$
$\Leftrightarrow 2x=\frac{784}{169}$
$\Leftrightarrow x=\frac{392}{169}$
b. ĐKXĐ: $x\geq 5$
PT $\Leftrightarrow \sqrt{4}.\sqrt{x-5}+\sqrt{x-5}-\frac{1}{3}.\sqrt{9}.\sqrt{x-5}=4$
$\Leftrightarrow 2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4$
$\Leftrightarrow 2\sqrt{x-5}=4$
$\Leftrightarrow \sqrt{x-5}=2$
$\Leftrightarrow x-5=4$
$\Leftrightarrow x=9$ (tm)
c. ĐKXĐ: $x\geq \frac{2}{3}$ hoặc $x< -1$
PT $\Leftrightarrow \frac{3x-2}{x+1}=9$
$\Rightarrow 3x-2=9(x+1)$
$\Leftrightarrow x=\frac{-11}{6}$ (tm)
S
22 tháng 3 2021
a, 3x - 7 = 0
<=> 3x = 7
<=> x = 7/3
b, 8 - 5x = 0
<=> -5x = -8
<=> x = 8/5
c, 3x - 2 = 5x + 8
<=> -2x = 10
<=> x = -5
22 tháng 3 2021
e) Ta có: \(\left(5x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=-1\\x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{5}\\x=3\end{matrix}\right.\)
Vậy: \(S=\left\{-\dfrac{1}{5};3\right\}\)
8 tháng 2 2022
a, \(\Rightarrow10x-4+6x=6+15-9x\Leftrightarrow7x=25\Leftrightarrow x=\dfrac{25}{7}\)
b, \(\Rightarrow2\left(3x^2+5x-2\right)-6x^2-3=33\Leftrightarrow10x-7=33\Leftrightarrow x=4\)
c, \(\Rightarrow12x-10x-4=21-9x\Leftrightarrow11x=25\Leftrightarrow x=\dfrac{25}{11}\)
d, \(\Rightarrow3x-3+2x-2-x+1=12\Leftrightarrow4x=16\Leftrightarrow x=4\)
19 tháng 2 2022
a: \(\Leftrightarrow7\left(7-3x\right)+12\left(5x+2\right)=84\left(x+13\right)\)
\(\Leftrightarrow49-21x+60x+24=84x+1092\)
\(\Leftrightarrow39x-84x=1092-73\)
=>-45x=1019
hay x=-1019/45
b: \(\Leftrightarrow21\left(x+3\right)-14=4\left(5x+9\right)-7\left(7x-9\right)\)
=>21x+63-14=20x+36-49x+63
=>21x+49=-29x+99
=>50x=50
hay x=1
c: \(\Leftrightarrow7\left(2x+1\right)-3\left(5x+2\right)=21x+63\)
=>14x+7-15x-6-21x-63=0
=>-22x-64=0
hay x=-32/11
d: \(\Leftrightarrow35\left(2x-3\right)-15\left(2x+3\right)=21\left(4x+3\right)-17\cdot105\)
=>70x-105-30x-45=84x+63-1785
=>40x-150-84x+1722=0
=>-44x+1572=0
hay x=393/11
a) \(5x-3=7\)
\(\Leftrightarrow5x=7+3\)
\(\Leftrightarrow5x=10\)
\(\Leftrightarrow x=\dfrac{10}{5}\)
\(\Leftrightarrow x=2\)
Vậy \(S=\left\{2\right\}\)
b) \(\left(x+3\right)\left(x-4\right)=0\)
\(\Leftrightarrow x+3=0\) hoặc \(x-4=0\)
*) \(x+3=0\)
\(x=0-3\)
\(x=-3\)
*) \(x-4=0\)
\(x=0+4\)
\(x=4\)
Vậy \(S=\left\{-3;4\right\}\)
c) \(\left|x^2+2014\right|=1\)
\(\Leftrightarrow x^2+2014=1\) hoặc \(x^2+2014=-1\)
*) \(x^2+2014=1\)
\(\Leftrightarrow x^2=1-2014\)
\(\Leftrightarrow x^2=-2013\) (vô lý)
*) \(x^2+2014=-1\)
\(\Leftrightarrow x^2=-1-2014\)
\(\Leftrightarrow x^2=-2015\) (vô lý)
Vậy \(S=\varnothing\)
d) \(\dfrac{2}{x+1}-\dfrac{1}{x-3}=\dfrac{3x-11}{x^2-2x-3}\) (1)
ĐKXĐ: \(x\ne-1;x\ne3\)
\(\left(1\right)\Leftrightarrow2\left(x-3\right)-\left(x+1\right)=3x-11\)
\(\Leftrightarrow2x-6-x-1=3x-11\)
\(\Leftrightarrow-2x=-11+7\)
\(\Leftrightarrow-2x=-4\)
\(\Leftrightarrow x=2\) (nhận)
Vậy \(S=\left\{2\right\}\)