Tìm x
x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + (x + 4 ) = 2020
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NM
0
BK
1
HV
18 tháng 1 2020
B=5+2(x-2019)2020
Vì (x-2019)2020 ≥0
=>5+(x-2019)2020 ≥5
Để B đạt Min
=>x-2019=0
=>x=2019
Vậy MinB=5 <=>x=2019
8 tháng 7 2021
\(3x\left(x-2020\right)-x+2020=0\)
\(3x\left(x-2020\right)-\left(x-2020\right)=0\)
\(\left(3x-1\right)\left(x-2020\right)=0\)
\(\orbr{\begin{cases}x=\frac{1}{3}\left(TM\right)\\x=2020\left(TM\right)\end{cases}}\)
\(b,4-9x^2=0\)
\(2^2-\left(3x\right)^2=0\)
\(\left(2-3x\right)\left(2+3x\right)=0\)
\(\orbr{\begin{cases}2-3x=0\\2+3x=0\end{cases}\orbr{\begin{cases}x=\frac{2}{3}\left(TM\right)\\x=-\frac{2}{3}\left(TM\right)\end{cases}}}\)
\(c,x^2-x+\frac{1}{4}=0\)
\(x^2-x+\left(\frac{1}{2}\right)^2=0\)
\(\left(x-\frac{1}{2}\right)^2=0\)
\(x-\frac{1}{2}=0\)
\(x=\frac{1}{2}\)
\(d,x\left(x-3\right)+\left(x-3\right)=0\)
\(\left(x-3\right)\left(x+1\right)=0\)
\(\orbr{\begin{cases}x-3=0\\x+1=0\end{cases}\orbr{\begin{cases}x=3\left(TM\right)\\x=-1\left(TM\right)\end{cases}}}\)
\(e,9x\left(x-7\right)-x+7=0\)
\(9x\left(x-7\right)-\left(x-7\right)=0\)
\(\left(9x-1\right)\left(x-7\right)=0\)
\(\orbr{\begin{cases}9x-1=0\\x-7=0\end{cases}\orbr{\begin{cases}x=\frac{1}{9}\left(TM\right)\\x=7\left(TM\right)\end{cases}}}\)
XO
8 tháng 7 2021
a) 3x(x - 2020) - x + 2020 = 0
<=> 3x(x - 2020) - (x - 2020) = 0
<=> (3x - 1)(x - 2020) = 0
<=> \(\orbr{\begin{cases}3x-1=0\\x-2020=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=2020\end{cases}}\)
Vậy tập nghiệm phương trình là \(S=\left\{\frac{1}{3};2020\right\}\)
b) \(4-9x^2=0\)
<=> \(\left(2-3x\right)\left(2+3x\right)=0\)
<=> \(\orbr{\begin{cases}2-3x=0\\2+3x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=-\frac{2}{3}\end{cases}}\)
Vậy \(x\in\left\{\frac{2}{3};-\frac{2}{3}\right\}\)là nghiệm phương trình
c) \(x^2-x+\frac{1}{4}=0\)
<=> \(\left(x-\frac{1}{2}\right)^2=0\)
<=> \(x-\frac{1}{2}=0\)
<=> \(x=\frac{1}{2}\)
d) x(x - 3) + (x - 3) = 0
<=> (x + 1)(x - 3) = 0
<=> \(\orbr{\begin{cases}x+1=0\\x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=3\end{cases}}\)
Vậy \(x\in\left\{-1;3\right\}\)là nghiệm phương trình
e) 9x(x - 7) - x + 7 = 0
<=> (9x - 1)(x - 7) = 0
<=> \(\orbr{\begin{cases}9x-1=0\\x-7=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{9}\\x=7\end{cases}}\)
Vậy \(x\in\left\{\frac{1}{9};7\right\}\)là nghiệm phương trình
CT
3
I
5 tháng 1 2023
\(\dfrac{x+1}{2023}+\dfrac{x+2}{2022}=\dfrac{x+3}{2021}+\dfrac{x+4}{2020}\\ \Leftrightarrow\dfrac{x+1}{2023}+1+\dfrac{x+2}{2022}+1=\dfrac{x+3}{2021}+1+\dfrac{x+4}{2020}+1\\ \Leftrightarrow\dfrac{x+1+2023}{2023}+\dfrac{x+2+2022}{2022}-\dfrac{x+3+2021}{2021}-\dfrac{x+4+2020}{2020}=0\\ \Leftrightarrow\left(x+2024\right)\times\left(\dfrac{1}{2023}+\dfrac{1}{2022}-\dfrac{1}{2021}-\dfrac{1}{2020}\right)=0\\ \Rightarrow x+2024=0:\left(\dfrac{1}{2023}+\dfrac{1}{2022}-\dfrac{1}{2021}-\dfrac{1}{2020}\right)\\ \Rightarrow x+2024=0\\ \Rightarrow x=-2024\)
20 tháng 8 2021
1, \(2x^3-50x=0\Leftrightarrow2x\left(x^2-25\right)=0\Leftrightarrow x=0;x=\pm5\)
2, \(5x^2-4\left(x^2-2x+1\right)-5=0\)
\(\Leftrightarrow5\left(x-1\right)\left(x+1\right)-4\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)\left[5\left(x+1\right)-4\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+9\right)=0\Leftrightarrow x=-9;x=1\)
3, \(6x\left(x-2\right)=x-2\Leftrightarrow\left(6x-1\right)\left(x-2\right)=0\Leftrightarrow x=\frac{1}{6};x=2\)
4, \(7\left(x-2020\right)^2-x+2020=0\Leftrightarrow7\left(x-2020\right)^2-\left(x-2020\right)=0\)
\(\Leftrightarrow\left(x-2020\right)\left[7\left(x-2020\right)-1\right]=0\Leftrightarrow x=2020;x=\frac{14141}{7}\)
5, \(x^2-10x=-25\Leftrightarrow x^2-10x+25=0\Leftrightarrow\left(x-5\right)^2=0\Leftrightarrow x=5\)
6, \(x^2-2x-3=0\Leftrightarrow\left(x+1\right)\left(x-3\right)=0\Leftrightarrow x=-1;x=3\)
20 tháng 8 2021
\(1,\)
\(2x^3-50x=0\)
\(\Leftrightarrow2x\left(x^2-25\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^2-25=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm5\end{cases}}\)
\(2,\)
\(5x^2-4\left(x^2-2x+1\right)-5=0\)
\(\Leftrightarrow5x^2-4x^2+8x-4-5=0\)
\(\Leftrightarrow x^2+8x-9=0\)
\(\Leftrightarrow x^2-x+9x-9=0\)
\(\Leftrightarrow x\left(x-1\right)+9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+9\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+9=0\\x-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-9\\x=1\end{cases}}\)
\(3,\)
\(6x\left(x-2\right)=x-2\)
\(\Leftrightarrow6x\left(x-2\right)-\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(6x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=\frac{1}{6}\end{cases}}\)
\(4,\)
\(7\left(x-2020\right)^2-x+2020=0\)
\(\Leftrightarrow7\left(x-2020\right)^2-\left(x-2020\right)=0\)
\(\Leftrightarrow\left(x-2020\right)[7\left(x-2020\right)-1]=0\)
\(\Leftrightarrow\left(x-2020\right)[7x-14141]=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=2020\\7x=14141\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2020\\x=\frac{14141}{7}\end{cases}}\)
\(5,\)
\(x^2-10x=-25\)
\(\Leftrightarrow x^2-10x+25=0\)
\(\Leftrightarrow\left(x-5\right)^2=0\)
\(\Leftrightarrow x-5=0\)
\(\Leftrightarrow x=5\)
\(6,\)
\(x^2-2x-3=0\)
\(\Leftrightarrow x^2-3x+x-3=0\)
\(\Leftrightarrow x\left(x-3\right)+\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\x+1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=-1\end{cases}}\)
SG
3
DN
2 tháng 5 2022
a) (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 2025
(x + x + x + x + x) + (1 + 2 + 3 + 4 + 5) = 2025
5x + 15 = 2025
5x = 2025 - 15
5x = 2010
x = 2010 : 5
x = 402
b) 5 * x - x = 2020
5 * x - x * 1 = 2020
x * (5 - 1) = 2020
x * 4 = 2020
x = 2020 : 4
x = 505
mong bạn tick
VN
2 tháng 5 2022
a) ( x + 1 ) + ( x + 2) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) = 2025
\(\left(x+x+x+x+x\right)+\left(1+2+3+4+5\right)=2025\)
\(5x+15=2025\)
\(5x=2025-15\)
\(5x=2010\)
\(x=2010:5\)
\(x=402\).
HK
2
C
20 tháng 3 2023
`x xx 6/7=5/14`
`=>x=5/14:6/7`
`=>x=5/14xx7/6`
`=>x=35/84`
`=>x=5/12`
Vậy `x=5/12`
__
`x:2/3=4/9`
`=>x=4/9xx2/3`
`=>x=8/27`
Vậy `x=8/27`
__
`x-1/4=3/2`
`=>x=3/2+1/4`
`=>x=6/4+1/4`
`=>x=7/4`
Vậy `x=7/4`
__
`x+4/5=8/9`
`=>x=8/9-4/5`
`=>x=40/45-36/45`
`=>x=4/45`
Vậy `x=4/45`
T
20 tháng 3 2023
\(x\cdot\dfrac{6}{7}=\dfrac{5}{14}\)
\(x\) \(=\dfrac{5}{14}:\dfrac{6}{7}\)
\(x\) \(=\dfrac{5}{12}\)
\(x:\dfrac{2}{3}=\dfrac{4}{9}\)
\(x\) \(=\dfrac{4}{9}\cdot\dfrac{2}{3}\)
\(x\) \(=\dfrac{8}{27}\)
\(x-\dfrac{1}{4}=\dfrac{3}{2}\)
\(x\) \(=\dfrac{3}{2}+\dfrac{1}{4}\)
\(x\) \(=\dfrac{7}{4}\)
\(x+\dfrac{4}{5}=\dfrac{8}{9}\)
\(x\) \(=\dfrac{8}{9}-\dfrac{4}{5}\)
\(x\) \(=\dfrac{4}{45}\)
x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 2020
x + x + 1 + x + 2 + x + 3 + x + 4 = 2020
5x + ( 1 + 2 + 3 + 4 ) = 2020
5x + 10 = 2020
5x = 2020 - 10
5x = 2010
x = 2010 : 5
x = 402
Giải:
Ta có: x+(x+1)+(x+2)+(x+3)+(x+4)=2020
=>x+x+1+x+2+x+3+x+4=2020
=>(x+x+x+x+x)+(1+2+3+4)=2020
=>5x+10=2020
=>5x=2020-10
=>5x=2010
=>x=2010:5
=>x=402
Vậy x=402