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Dùng công thức tính tổng
\(1+2+3+...+x=11325\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=11325\)
\(\Leftrightarrow x\left(x+1\right)=22650\)
\(\Leftrightarrow x\left(x+1\right)=150.151\)
Nên x = 150
Vậy ,,,
\(1+2+3+4+...+x=11325\)
\(\Rightarrow\frac{x\left(x+1\right)}{2}=11325\)
\(\Rightarrow x\left(x+1\right)=11325\times2\)
\(\Rightarrow x\left(x+1\right)=22650\)
\(\Rightarrow150\times151=22650\)
\(\Rightarrow x=150\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(5-x\right)^3=-64\)
\(\Leftrightarrow\left(5-x\right)^3=\left(-4\right)^3\)
\(\Leftrightarrow5-x=-4\)
\(\Leftrightarrow x=9\)
1)
( 5 - x )3 = - 64
( 5 - x )3 = ( - 4 )3
\(\Rightarrow\)5 - x = - 4
x = 5 - ( - 4 )
x = 5 + 4
x = 9
2)
A = 4 + 42 +43 + 44 + ........ + 499 + 4100
A = 4(4+1) + 43(4+1) + 45(4+1) + ........... + 499(4+1)
A = 4 . 5 + 43 . 5 + 45 . 5 + ............ + 499 . 5
A = 5(4+43 + 45 + ..........+ 499 )
Mà 5 \(⋮\) 5 \(\Rightarrow\) 5(4+43 + 45 + ........ + 499 ) \(⋮\) 5
Vậy A chia 5 dư 0
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, 3.(2\(x\) + 4) + 198 = (-3)2.10
3.(2\(x\) + 4) + 198 = 90
3.(2\(x\) + 4) = 90 - 198
3.(2\(x\) + 4) = - 108
2\(x\) + 4 = -108 : 3
2\(x\) + 4 = -36
2\(x\) = - 36 - 4
2\(x\) = - 40
\(x\) = -40 : 2
\(x\) = - 20
b, 2.(\(x\) + 7) - 6 = 18
2.(\(x\) + 7) = 18 + 6
2.(\(x\) + 7) =24
\(x\) + 7 = 24 : 2
\(x\) + 7 = 12
\(x\) = 12 - 7
\(x\) = 5
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(\frac{x}{5}-\frac{2}{3}+2x=\frac{1}{2}\)
\(\frac{6x}{30}-\frac{20}{30}+\frac{60x}{30}=\frac{15}{30}\)
\(\frac{66x-20}{30}=\frac{15}{30}\)
\(\Rightarrow\) 66x - 20 = 15
66x = 15 + 20
66x = 35
x = \(\frac{35}{66}\)
Vậy x = \(\frac{35}{66}\)
b, \(\frac{5}{2}-3\left(\frac{1}{3}-x\right)=\frac{1}{7}\)
\(\frac{5}{2}-1+3x=\frac{1}{7}\)
\(\frac{3}{2}+3x=\frac{1}{7}\)
3x = \(\frac{1}{7}-\frac{3}{2}\)
3x = \(\frac{-19}{14}\)
x = \(\frac{-19}{42}\)
Vậy x = \(\frac{-19}{42}\)
Phần c lỗi, chắc như thế này
c, \(4\cdot\left(\frac{1}{2}-x\right)+\frac{1}{2}=\frac{-5}{6}+x\)
\(2-4x+\frac{1}{2}=\frac{-5}{6}+x\)
\(\frac{5}{2}-4x=\frac{-5}{6}+x\)
\(-4x-x=\frac{-5}{6}-\frac{5}{2}\)
\(-5x=\frac{-10}{3}\)
x = \(\frac{2}{3}\)
Vậy x = \(\frac{2}{3}\)
Chúc bn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3\left(x-5\right)-2\left(x+4\right)=-1\)
\(\Rightarrow3x-15-2x-8=-1\)
\(\Rightarrow3x-2x=-1+8+15\)
\(\Rightarrow x=22\)
\(\left|x-3\right|-5^2=\left(-5\right).4\)
\(\Rightarrow\left|x-3\right|=5\)
\(\Rightarrow\orbr{\begin{cases}x-3=5\\x-3=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=8\\x=-2\end{cases}}\)
\(-14-2\left|x-5\right|=0\)
\(\Rightarrow2\left|x-5\right|=-14\)
Vì \(\left|x\right|\ge0\Rightarrow2\left|x-5\right|=-14\)(vô lí)
\(\left(3x+1\right)^2=49\)
\(\Rightarrow\left(3x+1\right)^2=\left(\pm7\right)^2\)
\(\Rightarrow\orbr{\begin{cases}3x+1=7\\3x+1=-7\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-\frac{8}{3}\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
Ta có: \(4-2\left(x+1\right)=2\)
\(\Leftrightarrow2\left(x+1\right)=2\)
\(\Leftrightarrow x+1=1\)
hay x=0
Bài 2:
Ta có: \(\left|2x-3\right|-1=2\)
\(\Leftrightarrow\left|2x-3\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
Ta có: (x-1+1)(x+1)=11325
=>x(x+1) : 2=11325
=>x(x+1)=11325 x 2=22650
Mà x và x+1 là hai số tự nhiên liên tiếp.
Phân tích 22650 ra thừa số nguyên tố
22650=2 x 3 x 52 x 151
22650=(2 x 3 x 25) x 151
22650=150 x 151
=> x=150