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\(\dfrac{1}{2x}+\dfrac{1}{2\left(25-x\right)}=\dfrac{1}{12}\)
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DN
1
8 tháng 4 2023
=>\(\dfrac{8}{x}+\dfrac{8}{y}+\dfrac{20}{3}\cdot\dfrac{1}{y}=1\)
=>\(\dfrac{8}{x}+\dfrac{44}{3y}=1\)
=>\(\dfrac{24y+44x}{3xy}=1\)
=>44x+24y=3xy
=>44x+24y-3xy=0
=>44x-3y(x-8)=0
=>44x-352-3y(x-8)=352
=>(x-8)(44-3y)=352
=>\(\left(x-8;44-3y\right)\in\left\{\left(32;11\right)\left(44;8\right);\left(176;2\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(40;11\right);\left(52;12\right);\left(184;14\right)\right\}\)
14 tháng 4 2023
a: =>11(x-3)=6(x-5)
=>11x-33=6x-30
=>5x=3
=>x=3/5
b: =>(4/3-1/4x-5/12)-2x=8/5*5/3=8/3
=>-9/4x+11/12=8/3
=>-9/4x=32/12-11/12=21/12=7/4
=>x=-7/9
c: =>1/2x-1/3-2/3x-1=x
=>-1/6x-4/3=x
=>-7/6x=4/3
=>x=-4/3:7/6=-4/3*6/7=-24/21=-8/7
d: =>1-2x-3x+1=7/2
=>-5x=3/2
=>x=-3/10
21 tháng 2 2023
a: \(\Leftrightarrow x^2+x+1-3x^2=2x\left(x-1\right)\)
=>-2x^2+x+1-2x^2+2x=0
=>-4x^2+3x+1=0
=>4x^2-3x-1=0
=>4x^2-4x+x-1=0
=>(x-1)(4x+1)=0
=>x=1(loại) hoặc x=-1/4(nhận)
b: \(\Leftrightarrow\dfrac{440}{x-2}-\dfrac{440}{x}=1\)
=>x(x-2)=440x-440x+880
=>x^2-2x-880=0
=>\(x=1\pm\sqrt{881}\)
c: \(\Leftrightarrow\dfrac{x+5+x}{x\left(x+5\right)}=\dfrac{1}{6}\)
=>x^2+5x=6(2x+5)
=>x^2+5x-12x-30=0
=>x^2-7x-30=0
=>(x-10)(x+3)=0
=>x=10 hoặc x=-3
d: =>(x-1)(x+1)-x=2x-1
=>x^2-1-x=2x-1
=>x^2-x-2x=0
=>x(x-3)=0
=>x=0(loại) hoặc x=3(nhận)
10 tháng 5 2022
1: \(\left(3x-\dfrac{1}{5}\right)^2=\left(-\dfrac{3}{25}\right)^2\)
=>3x-1/5=3/25 hoặc 3x-1/5=-3/25
=>3x=8/25 hoặc 3x=2/25
=>x=8/75 hoặc x=2/75
2: \(\left(2x-\dfrac{1}{3}\right)^2=\left(-\dfrac{2}{9}\right)^2\)
=>2x-1/3=2/9 hoặc 2x-1/3=-2/9
=>2x=5/9 hoặc 2x=1/9
=>x=5/18 hoặc x=1/18
LN
1
27 tháng 12 2021
\(=\dfrac{x+12+x-2}{x-2}\cdot\dfrac{x\left(x-2\right)}{\left(5-x\right)\left(5+x\right)}=\dfrac{2x\left(x+5\right)}{\left(5-x\right)\left(5+x\right)}=\dfrac{2x}{5-x}\)
25 tháng 1 2022
4, \(\Leftrightarrow4x+4+9\left(2x+1\right)=4x+6\left(x+1\right)+7+12x\)
\(\Leftrightarrow22x+13=22x+13\)vậy pt có vô số nghiệm
5, \(\dfrac{2x}{3}+\dfrac{2x-1}{6}=4-\dfrac{x}{3}\Rightarrow4x+2x-1=24-2x\)
\(\Leftrightarrow8x=25\Leftrightarrow x=\dfrac{25}{8}\)
6, \(\dfrac{x-1}{2}+\dfrac{x-1}{4}=1-\dfrac{2\left(x-1\right)}{3}\Rightarrow6x-6+3x-3=12-8\left(x-1\right)\)
\(\Leftrightarrow9x-9=20-8x\Leftrightarrow17x=29\Leftrightarrow x=\dfrac{29}{17}\)
4 tháng 3 2022
a: \(\Leftrightarrow4\left(5x^2-3\right)+5\left(3x-1\right)< 10x\left(2x+3\right)-100\)
\(\Leftrightarrow20x^2-12x+15x-5< 20x^2+30x-100\)
=>3x-5<=30x-100
=>30x-100>3x-5
=>27x>95
hay x>95/27
b: \(\Leftrightarrow4\left(5x-2\right)-6\left(2x^2-x\right)< 4x\left(1-3x\right)-15x\)
\(\Leftrightarrow20x-8-12x^2+6x< 4x-12x^2-15x\)
=>26x-8<-11x
=>37x<8
hay x<8/37
H9
HT.Phong (9A5)
CTVHS
11 tháng 7 2023
d) \(\left(x+2\right)\left(x^2-2x+4\right)\)
\(=\left(x+2\right)\left(x^2-2\cdot x+2^2\right)\)
\(=x^3+2^3\)
\(=x^3+8\)
e) \(\left(\dfrac{1}{4}-\dfrac{x}{5}\right)\left(\dfrac{x^2}{25}+\dfrac{x}{20}+\dfrac{1}{16}\right)\)
\(=\left(\dfrac{1}{4}-\dfrac{1}{5}x\right)\left(\dfrac{1}{25}x^2+\dfrac{1}{5}x\cdot\dfrac{1}{4}+\dfrac{1}{16}\right)\)
\(=\left(\dfrac{1}{4}-\dfrac{1}{5}x\right)\left[\left(\dfrac{1}{5}x\right)^2+\dfrac{1}{5}x\cdot\dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2\right]\)
\(=\left(\dfrac{1}{4}\right)^3-\left(\dfrac{1}{5}x\right)^3\)
\(=\dfrac{1}{64}-\dfrac{1}{125}x^3\)
\(=\dfrac{1}{64}-\dfrac{x^3}{125}\)
10 tháng 7 2023
d: (x+2)(x^2-2x+4)
=(x+2)(x^2-x*2+2^2)
=x^3+8
e: (1/4-x/5)(1/16+x/20+x^2/25)
=(1/4-x/5)[(1/4)^2+1/4*x/5+(x/5)^2]
=1/64-x^3/125
AH
Akai Haruma
Giáo viên
3 tháng 8 2021
a. ĐKXĐ: $x\geq 1$
PT $\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{3}{2}.\sqrt{9}.\sqrt{x-1}+24.\sqrt{\frac{1}{64}}.\sqrt{x-1}=-17$
$\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17$
$\Leftrightarrow -\sqrt{x-1}=-17$
$\Leftrightarrow \sqrt{x-1}=17$
$\Leftrightarrow x-1=289$
$\Leftrightarrow x=290$
b. ĐKXĐ: $x\geq \frac{1}{2}$
PT $\Leftrightarrow \sqrt{9}.\sqrt{2x-1}-0,5\sqrt{2x-1}+\frac{1}{2}.\sqrt{25}.\sqrt{2x-1}+\sqrt{49}.\sqrt{2x-1}=24$
$\Leftrightarrow 3\sqrt{2x-1}-0,5\sqrt{2x-1}+2,5\sqrt{2x-1}+7\sqrt{2x-1}=24$
$\Leftrightarrow 12\sqrt{2x-1}=24$
$\Leftrihgtarrow \sqrt{2x-1}=2$
$\Leftrightarrow x=2,5$ (tm)
AH
Akai Haruma
Giáo viên
3 tháng 8 2021
c. ĐKXĐ: $x\geq 2$
PT $\Leftrightarrow \sqrt{36}.\sqrt{x-2}-15\sqrt{\frac{1}{25}}\sqrt{x-2}=4(5+\sqrt{x-2})$
$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$
$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)
Vậy pt vô nghiệm
ĐKXĐ: \(\left\{{}\begin{matrix}2x\ne0\\2\left(25-x\right)\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne25\end{matrix}\right.\)
\(\dfrac{1}{2x}+\dfrac{1}{2\left(25-x\right)}=\dfrac{1}{12}\\ \Leftrightarrow\dfrac{25-x+x}{2x\left(25-x\right)}=\dfrac{1}{12}\\ \Leftrightarrow\dfrac{25}{-2x^2+50x}=\dfrac{1}{12}\\ \Leftrightarrow-2x^2+50x=300\\ \Leftrightarrow-2x^2+50x-300=0\\ \Leftrightarrow\left[{}\begin{matrix}x=15\left(tm\right)\\x=10\left(tm\right)\end{matrix}\right.\)
Vậy...