12. Giải các phương trình:
(x+1) +(2x+3) +(3x+5) +... +(50x+99) =5050
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
NL
Nguyễn Lê Phước Thịnh
CTVHS
28 tháng 6
a: \(2x^3-50x=0\)
=>\(2x\left(x^2-25\right)=0\)
=>x(x-5)(x+5)=0
=>x∈{0;5;-5}
b: \(2x\left(3x-5\right)-\left(5-3x\right)=0\)
=>2x(3x-5)+(3x-5)=0
=>(3x-5)(2x+1)=0
=>\(\left[\begin{array}{l}3x-5=0\\ 2x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac53\\ x=-\frac12\end{array}\right.\)
c: \(9\left(3x-2\right)=x\left(2-3x\right)\)
=>9(3x-2)-x(2-3x)=0
=>9(3x-2)+x(3x-2)=0
=>(3x-2)(x+9)=0
=>\(\left[\begin{array}{l}3x-2=0\\ x+9=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac23\\ x=-9\end{array}\right.\)
d: \(\left(2x-1\right)^2-25=0\)
=>(2x-1-5)(2x-1+5)=0
=>(2x-6)(2x+4)=0
=>(x-3)(x+2)=0
=>\(\left[\begin{array}{l}x-3=0\\ x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=-2\end{array}\right.\)
e: \(25x^2-2=0\)
=>\(25x^2=2\)
=>\(x^2=\frac{2}{25}\)
=>\(\left[\begin{array}{l}x=\frac{\sqrt2}{5}\\ x=-\frac{\sqrt2}{5}\end{array}\right.\)
f: \(x^2-25=6x-9\)
=>\(x^2-6x-16=0\)
=>(x-8)(x+2)=0
=>\(\left[\begin{array}{l}x-8=0\\ x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=8\\ x=-2\end{array}\right.\)
g: 5x(x-3)-2x+6=0
=>5x(x-3)-2(x-3)=0
=>(x-3)(5x-2)=0
=>\(\left[\begin{array}{l}x-3=0\\ 5x-2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=\frac25\end{array}\right.\)
h: 3x(x-7)-2(x-7)=0
=>(x-7)(3x-2)=0
=>\(\left[\begin{array}{l}x-7=0\\ 3x-2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=7\\ x=\frac23\end{array}\right.\)
i: \(7x^2-28=0\)
=>\(7x^2=28\)
=>\(x^2=4\)
=>x=2 hoặc x=-2
j: 2x+1+x(2x+1)=0
=>(2x+1)(x+1)=0
=>\(\left[\begin{array}{l}2x+1=0\\ x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-\frac12\\ x=-1\end{array}\right.\)
k: \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
=>(x+2)(x+2-x+2)=0
=>4(x+2)=0
=>x+2=0
=>x=-2
l: \(x^3+5x^2-4x-20=0\)
=>\(x^2\left(x+5\right)-4\left(x+5\right)=0\)
=>\(\left(x+5\right)\left(x^2-4\right)=0\)
=>(x+5)(x-2)(x+2)=0
=>x∈{-5;2;-2}
m: \(x^2-25+2\left(x+5\right)=0\)
=>(x-5)(x+5)+2(x+5)=0
=>(x+5)(x-3)=0
=>\(\left[\begin{array}{l}x+5=0\\ x-3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-5\\ x=3\end{array}\right.\)
n: \(x^2-3x+2=0\)
=>\(x^2-x-2x+2=0\)
=>x(x-1)-2(x-1)=0
=>(x-1)(x-2)=0
=>\(\left[\begin{array}{l}x-1=0\\ x-2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1\\ x=2\end{array}\right.\)
o: \(x^2-6x+8=0\)
=>\(\left(x-2\right)\left(x-4\right)=0\)
=>\(\left[\begin{array}{l}x-2=0\\ x-4=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2\\ x=4\end{array}\right.\)
p: \(x^2-5x-14=0\)
=>\(x^2-7x+2x-14=0\)
=>(x-7)(x+2)=0
=>\(\left[\begin{array}{l}x-7=0\\ x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=7\\ x=-2\end{array}\right.\)
q: \(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\)
=>\(x^2-4x+4-x^2+9=6\)
=>-4x+13=6
=>-4x=6-13=-7
=>x=7/4
r: \(\left(2x-1\right)^2-\left(2x-5\right)\left(2x+5\right)=18\)
=>\(4x^2-4x+1-\left(4x^2-25\right)=18\)
=>-4x+26=18
Y
12 tháng 4 2022
\(a,\dfrac{x-3}{x}=\dfrac{x-3}{x+3}\)\(\left(đk:x\ne0,-3\right)\)
\(\Leftrightarrow\dfrac{x-3}{x}-\dfrac{x-3}{x+3}=0\)
\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+3\right)-x\left(x-3\right)}{x\left(x+3\right)}=0\)
\(\Leftrightarrow x^2-9-x^2+3x=0\)
\(\Leftrightarrow3x-9=0\)
\(\Leftrightarrow3x=9\)
\(\Leftrightarrow x=3\left(n\right)\)
Vậy \(S=\left\{3\right\}\)
Y
12 tháng 4 2022
\(b,\dfrac{4x-3}{4}>\dfrac{3x-5}{3}-\dfrac{2x-7}{12}\)
\(\Leftrightarrow\dfrac{4x-3}{4}-\dfrac{3x-5}{3}+\dfrac{2x-7}{12}>0\)
\(\Leftrightarrow\dfrac{3\left(4x-3\right)-4\left(3x-5\right)+2x-7}{12}>0\)
\(\Leftrightarrow12x-9-12x+20+2x-7>0\)
\(\Leftrightarrow2x+4>0\)
\(\Leftrightarrow2x>-4\)
\(\Leftrightarrow x>-2\)
9 tháng 1 2023
a. 3(x-2)-10=5(2x + 1)
<=> 3x - 6 - 10 = 10x + 5
<=> 3x - 10x = 5 + 6 + 10
<=> -7x = 21
<=> x = -3
b. 3x + 2=8 -2(x-7)
<=> 3x + 2 = 8 - 2x + 14
<=> 3x + 2x = 8 + 14 - 2
<=> 5x = 20
<=> x = 4
c. 2x-(2+5x)= 4(x + 3)
<=> 2x - 2 - 5x = 4x + 12
<=> 2x - 5x - 4x = 12 + 2
<=> -7x = 14
<=> x = -2
d. 5-(x +8)=3x + 3(x-9)
<=> 5 - x - 8 = 3x + 3x - 27
<=> -x - 3x - 3x = -27 + 8 - 5
<=> -7x = -24
<=> x = 24/7
e. 3x - 18 + x= 12-(5x + 3)
<=> 3x - 18 + x = 12 - 5x - 3
<=> 3x + x - 5x = 12 - 3 + 18
<=> -x = 27
<=> x = - 27
9 tháng 1 2023
a. 3(x-2)-10=5(2x + 1)
<=> 3x - 6 - 10 = 10x + 5
<=> 3x - 10x = 5 + 6 + 10
<=> -7x = 21
<=> x = -3
b. 3x + 2=8 -2(x-7)
<=> 3x + 2 = 8 - 2x + 14
<=> 3x + 2x = 8 + 14 - 2
<=> 5x = 20
<=> x = 4
c. 2x-(2+5x)= 4(x + 3)
<=> 2x - 2 - 5x = 4x + 12
<=> 2x - 5x - 4x = 12 + 2
<=> -7x = 14
<=> x = -2
d. 5-(x +8)=3x + 3(x-9)
<=> 5 - x - 8 = 3x + 3x - 27
<=> -x - 3x - 3x = -27 + 8 - 5
<=> -7x = -24
<=> x = 24/7
e. 3x - 18 + x= 12-(5x + 3)
<=> 3x - 18 + x = 12 - 5x - 3
<=> 3x + x - 5x = 12 - 3 + 18
<=> -x = 27
<=> x = - 27
TM
11 tháng 8 2021
1/ \(7x-5=13-5x\)
\(\Leftrightarrow12x=18\)
\(\Leftrightarrow x=\dfrac{3}{2}\)
Vậy: \(S=\left\{\dfrac{3}{2}\right\}\)
==========
2/ \(19+3x=5-18x\)
\(\Leftrightarrow21x=-14\)
\(\Leftrightarrow x=-\dfrac{2}{3}\)
Vậy: \(S=\left\{-\dfrac{2}{3}\right\}\)
==========
3/ \(x^2+2x-4=-12+3x+x^2\)
\(\Leftrightarrow-x=-8\)
\(\Leftrightarrow x=8\)
Vậy: \(S=\left\{8\right\}\)
===========
4/ \(-\left(x+5\right)=3\left(x-5\right)\)
\(\Leftrightarrow-x-5=3x-15\)
\(\Leftrightarrow-4x=-10\)
\(\Leftrightarrow x=\dfrac{5}{2}\)
Vậy: \(S=\left\{\dfrac{5}{2}\right\}\)
==========
5/ \(3\left(x+4\right)=\left(-x+4\right)\)
\(\Leftrightarrow3x+12=-x+4\)
\(\Leftrightarrow4x=-8\)
\(\Leftrightarrow x=-2\)
Vậy: \(S=\left\{-2\right\}\)
[----------]
NT
11 tháng 8 2021
1. \(7x-5=13-5x\) \(\Leftrightarrow12x=18\Leftrightarrow x=\dfrac{3}{2}\)
2. \(19+3x=5-18x\Leftrightarrow21x=-14\Leftrightarrow x=-\dfrac{2}{3}\)
3. \(x^2+2x-4=-12+3x+x^2\Leftrightarrow-x=-8\Leftrightarrow x=8\)
4. \(-\left(x+5\right)=3\left(x-5\right)\Leftrightarrow-x-5=3x-15\Leftrightarrow4x=10\Leftrightarrow x=\dfrac{5}{2}\)
5. \(3\left(x+4\right)=-x+4\Leftrightarrow3x+12=-x+4\Leftrightarrow4x=-8\Leftrightarrow x=-2\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
17 tháng 9 2025
a: \(27x^2\left(x+3\right)-12\left(x^2+3x\right)=0\)
=>\(27x^2\left(x+3\right)-12x\left(x+3\right)=0\)
=>\(\left(x+3\right)\cdot\left(27x^2-12x\right)=0\)
=>3x(x+3)(9x-4)=0
=>x(x+3)(9x-4)=0
=>\(\left[\begin{array}{l}x=0\\ x+3=0\\ 9x-4=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-3\\ x=\frac49\end{array}\right.\)
b: \(\left(x-2\right)\left(3x+5\right)=\left(2x-4\right)\left(x+1\right)\)
=>\(\left(x-2\right)\left(3x+5\right)=2\left(x-2\right)\left(x+1\right)\)
=>(x-2)(3x+5)-(x-2)(2x+2)=0
=>(x-2)(3x+5-2x-2)=0
=>(x-2)(x+3)=0
=>\(\left[\begin{array}{l}x-2=0\\ x+3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2\\ x=-3\end{array}\right.\)
c: \(2\left(9x^2+6x+1\right)=\left(3x+1\right)\left(x-2\right)\)
=>\(2\left(3x+1\right)^2-\left(3x+1\right)\left(x-2\right)=0\)
=>(3x+1)(6x+2)-(3x+1)(x-2)=0
=>(3x+1)(6x+2-x+2)=0
=>(3x+1)(5x+4)=0
=>\(\left[\begin{array}{l}3x+1=0\\ 5x+4=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-\frac13\\ x=-\frac45\end{array}\right.\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
13 tháng 5 2023
2:
a: =>-2x=10
=>x=-5
b: =>(x-3)(2x+5)=0
=>x=3 hoặc x=-5/2
2 tháng 2 2022
a) \(PT\Leftrightarrow3x-2x=2-3\Leftrightarrow x=-1\)
Vậy: \(S=\left\{-1\right\}\)
b) \(PT\Leftrightarrow-2x+3x=-7+22\Leftrightarrow x=15\)
Vậy: \(S=\left\{15\right\}\)
c) \(PT\Leftrightarrow8x-5x=3+12\Leftrightarrow3x=15\Leftrightarrow x=5\)
Vậy: \(S=\left\{5\right\}\)
d) \(PT\Leftrightarrow x+4x-2x=12+25-1\Leftrightarrow3x=36\Leftrightarrow x=12\)
Vậy: \(S=\left\{12\right\}\)
e) \(PT\Leftrightarrow x+2x+3x-3x=19+5\Leftrightarrow3x=24\Leftrightarrow x=8\)
Vậy: \(S=\left\{8\right\}\)
TD
2 tháng 2 2022
a)3x-2=2x-3
=>x=-1
b)7-2x=22-3x
=>x=15
c)8x-3=5x+12
=>3x=15
=>x=5
d)x-12+4x=25+2x-1
=>3x=12
=>x=4
e)x+2x+3x-19=3x+5
=>3x=24
=>x=8
Số số hạng là (50-1):1+1=50(số)
Tổng của các hệ số tự do là (1+99)*50/2=50^2=2500
Tổng của các hệ số chứa biến là:
(50+1)*50/2=25*51=1275
=>1275x+2500=5050
=>1275x=2550
=>x=2