giải PT
2x=7+x
x-6=2x
3x+1=5x+2
4x-3=2x+2
2(x-3)12
3(x+4)=6
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PN
17 tháng 8 2020
a, \(12-2\left(1-x\right)^2=\left(3x-2\right)\left(2x-3\right)\)
\(< =>12-2\left(1-2x+x^2\right)=6x^2-9x-4x+6\)
\(< =>12-2+4x-2x^2=6x^2-13x+6\)
\(< =>10+4x-2x^2-6x^2+13x-6=0\)
\(< =>-8x^2+17x+4=0< =>\orbr{\begin{cases}x=\frac{17-\sqrt{417}}{16}\\x=\frac{17+\sqrt{417}}{16}\end{cases}}\)
b, \(10x+3-5x=4x+12< =>5x+3-4x-12=0\)
\(< =>x-9=0< =>x=9\)
c, \(11x+42-2x=100-9x-22< =>9x+42-100+9x+22=0\)
\(< =>18x+64-100=0< =>18x-36=0< =>x=\frac{36}{18}=2\)
d, \(2x-\left(3-5x\right)=4\left(x+3\right)< =>2x-3+5x=4x+12\)
\(< =>7x-3-4x-12=0< =>3x-15=0< =>x=\frac{15}{3}=5\)
e, \(2\left(x-3\right)+5x\left(x-1\right)=5x^2< =>2x-6+5x^2-5=5x^2\)
\(< =>2x-11+5x^2-5x^2=0< =>2x-11=0< =>x=\frac{11}{2}\)
f, \(-6\left(1,5-2x\right)=3\left(-15+2x\right)< =>-6\left(\frac{3}{2}-2x\right)=3\left(2x-15\right)\)
\(< =>-9+12x-6x+45=0< =>6x+36=0< =>x=-6\)
g, \(14x-\left(2x+7\right)=3x+12x-13< =>14x-2x-7=15x-13\)
\(< =>12x-7-15x+13=0< =>-3x+6=0< =>x=-2\)
h, \(\left(x-4\right)\left(x+4\right)-2\left(3x-2\right)=\left(x-4\right)^2\)
\(< =>x^2-16-6x+4=x^2-8x+16\)
\(< =>x^2-6x-12-x^2+8x-16=0\)
\(< =>2x-28=0< =>x=\frac{28}{2}=14\)
q, \(4\left(x-2\right)-\left(x-3\right)\left(2x-5\right)=?\)thiếu đề
LT
2
LT
5 tháng 6 2020
(x - 1)(2x² - 10) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\2x^2-10=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\2x^2=10\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\sqrt{5}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm là: \(S=\left\{1;\sqrt{5}\right\}\)
(2x - 7)2 - 6(2x - 7)(x - 3) = 0
\(\Leftrightarrow\left(2x-7\right)\left(2x-7-6x+18\right)=0\)
\(\Leftrightarrow\left(2x-7\right)\left(11-4x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-7=0\\11-4x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=7\\4x=11\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{7}{2}\\x=\frac{11}{4}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm là: \(S=\left\{\frac{7}{2};\frac{11}{4}\right\}\)
(5x + 3)(x2 + 4) = 0
\(\Leftrightarrow\left[{}\begin{matrix}5x+3=0\\x^2+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=-3\\x^2=-4\left(Loại\right)\end{matrix}\right.\)
\(\Leftrightarrow x=-\frac{3}{5}\)
Vậy phương trình có tập nghiệm là: \(S=\left\{-\frac{3}{5}\right\}\)
5 tháng 6 2020
a)
\(\left(x-1\right)\cdot\left(2x^2-10\right)=0\\ \Leftrightarrow\left(x-1\right)\cdot2\cdot\left(x^2-5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-1=0\\x^2-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=\pm\sqrt{5}\end{matrix}\right.\)
b)
\(\left(2x-7\right)^2-6\cdot\left(6x-7\right)\cdot\left(x-3\right)=0\\ \Leftrightarrow\left(2x-7\right)\cdot\left[\left(2x-7\right)-6\cdot\left(x-3\right)\right]=0\\ \Leftrightarrow\left(2x-7\right)\cdot\left(2x-7-6x+18\right)=0\\ \Leftrightarrow\left(2x-7\right)\cdot\left(11-4x\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x-7=0\\11-4x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{7}{2}\\x=\frac{11}{4}\end{matrix}\right.\)
c)
\(\left(5x+3\right)\cdot\left(x^2+4\right)=0\)
Vì \(\left(x^2+4\right)>0\Rightarrow\left(loại\right)\)
\(\Rightarrow5x+3=0\\ \Rightarrow x=-\frac{3}{5}\)
19 tháng 4 2020
c)
\(x^2-x-12=0\\ \Leftrightarrow x^2+3x-4x-12=0\\ \Leftrightarrow x\cdot\left(x+3\right)-4\cdot\left(x+3\right)=0\\ \Leftrightarrow\left(x-4\right)\cdot\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
e)
\(\frac{6x+22}{x+2}-\frac{2x+7}{x+3}=\frac{x+4}{x^2+5x+6}\\ \Leftrightarrow\frac{6x^2+40x+66}{x^2+5x+6}-\frac{2x^2+11x+14}{x^2+5x+6}-\frac{x+4}{x^2+5x+6}=0\\ \Leftrightarrow6x^2+40x+66-2x^2-11x-14-x-4=0\\ \Leftrightarrow4x^2+28x+48=0\\ \Leftrightarrow4\cdot\left(x^2+7x+12\right)=0\\ \Leftrightarrow4\cdot\left(x^4+4x+3x+12\right)=0\\ \Leftrightarrow4\cdot\left[x\cdot\left(x+4\right)+3\cdot\left(x+4\right)\right]=0\\ \Leftrightarrow4\cdot\left(x+4\right)\cdot\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+4=0\\x+3=0\end{matrix}\right.\Rightarrow}\left\{{}\begin{matrix}x=-4\\x=-3\end{matrix}\right.\)
19 tháng 4 2020
b)
\(\frac{4x}{x^2+4x+3}-1=6\cdot\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\\ \Leftrightarrow\frac{4x}{\left(x+1\right)\cdot\left(x+3\right)}-1=6\cdot\left(\frac{1}{x+3}-\frac{1}{2\cdot\left(x+1\right)}\right)\\ \Leftrightarrow4x-\left(x+1\right)\cdot\left(x+3\right)=6\cdot\left(\frac{1}{x+3}-\frac{1}{2\cdot\left(x+2\right)}\right)\cdot\left(x+1\right)\cdot\left(x+3\right)\\ \Leftrightarrow-x^2-3=\frac{6x^2}{x+3}+\frac{24x}{x+3}+\frac{18}{x+3}-\frac{3x^2}{x+1}-\frac{12x}{x+1}-\frac{9}{x++1}\\ \Leftrightarrow-x^2\cdot\left(x+3\right)\cdot\left(x+1\right)-3\cdot\left(x+3\right)\cdot\left(x+1\right)=6x^2\cdot\left(x+1\right)+24x\cdot\left(x+1\right)+18\cdot\left(x+1\right)-3x^2\cdot\left(x+3\right)-12x\cdot\left(x+3\right)-9\cdot\left(x+3\right)\\ \Leftrightarrow-x^4-4x^3-6x^2-12x-9=3x^3+9x^2-3x-9\\ \Leftrightarrow-x^4-4x^3-6x^2-12x=3x^3+9x^2-3x\\ \Leftrightarrow x^4+4x^3+6x^2+12x+3x^3+9x^2-3x=0\\ \Leftrightarrow x^4+7x^3+15x^2+9x=0\\ \Leftrightarrow x\cdot\left(x^3+7x^2+15x+9\right)=0\\ \Leftrightarrow x\cdot\left(x^2+6x+9\right)\cdot\left(x+1\right)=0\\ \Leftrightarrow x\cdot\left(x+3\right)^2\cdot\left(x+1\right)=0\)
\(\Rightarrow x=\left[{}\begin{matrix}0\\-3\\-1\end{matrix}\right.\)
HT
1
15 tháng 3 2022
\(5x-4\left(6x+18-x^2-3x\right)=\left(12-8x-6x+4x^2\right)+2\)
\(\Leftrightarrow5x-4\left(-x^2+3x+18\right)=\left(4x^2-14x+12\right)+2\)
\(\Leftrightarrow4x^2-7x-72=4x^2-14x+14\Leftrightarrow7x=86\Leftrightarrow x=\dfrac{86}{7}\)
10 tháng 2 2020
1) Ta có: 3x-12=5x(x-4)
\(\Leftrightarrow3x-12-5x\left(x-4\right)=0\)
\(\Leftrightarrow3x-12-5x^2+20x=0\)
\(\Leftrightarrow-5x^2+23x-12=0\)
\(\Leftrightarrow-5x^2+20x+3x-12=0\)
\(\Leftrightarrow\left(-5x^2+20x\right)+\left(3x-12\right)=0\)
\(\Leftrightarrow5x\left(-x+4\right)+3\left(x-4\right)=0\)
\(\Leftrightarrow5x\left(4-x\right)-3\left(4-x\right)=0\)
\(\Leftrightarrow\left(4-x\right)\left(5x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4-x=0\\5x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\5x=3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\frac{3}{5}\end{matrix}\right.\)
Vậy: \(x\in\left\{4;\frac{3}{5}\right\}\)
2) Ta có: 3x-15=2x(x-5)
\(\Leftrightarrow3x-15-2x\left(x-5\right)=0\)
\(\Leftrightarrow3\left(x-5\right)-2x\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(3-2x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\3-2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\2x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\frac{3}{2}\end{matrix}\right.\)
Vậy: \(x\in\left\{5;\frac{3}{2}\right\}\)
3) Ta có: 3x(2x-3)+2(2x-3)=0
\(\Leftrightarrow\left(2x-3\right)\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\3x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{3}{2}\\x=\frac{-2}{3}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{3}{2};-\frac{2}{3}\right\}\)
4) Ta có: (4x-6)(3-3x)=0
\(\Leftrightarrow\left[{}\begin{matrix}4x-6=0\\3-3x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=6\\3x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{6}{4}=\frac{3}{2}\\x=1\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{3}{2};1\right\}\)
10 tháng 2 2020
4) (4x - 6 ) ( 3 - 3x ) = 0
<=> \(\left[{}\begin{matrix}4x-6=0\\3-3x=0\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}4x=6\\3x=3\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=\frac{3}{2}\\x=1\end{matrix}\right.\)
ta có 2x =7+x
->2x+x =7
->3x =7
->x =7/3
vậy x =7/3