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A
19 tháng 10 2020
a, \(x\left(x+1\right)-x\left(x-5\right)=6\Leftrightarrow x^2+x-x^2+5x=6\)
\(\Leftrightarrow x=1\)
b, \(4x^2-4x+1=0\Leftrightarrow\left(2x-1\right)^2=0\Leftrightarrow x=\frac{1}{2}\)
c, \(x^2-\frac{1}{4}=0\Leftrightarrow\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)=0\Leftrightarrow x=\pm\frac{1}{2}\)
d, \(5x^2=20x\Leftrightarrow5x^2-20x=0\Leftrightarrow5x\left(x-4\right)=0\Leftrightarrow x=0;4\)
e, \(4x^2-9-x\left(2x-3\right)=0\Leftrightarrow4x^2-9-2x^2=3x\Leftrightarrow2x^2-9-3x=0\)
\(\Leftrightarrow\left(2x+3\right)\left(x-3\right)=0\Leftrightarrow x=-\frac{3}{2};3\)
f, \(4x^2-25=\left(2x-5\right)\left(2x+7\right)\Leftrightarrow\left(2x-5\right)\left(2x+5\right)-\left(2x-5\right)\left(2x+7\right)=0\)
\(\Leftrightarrow-2\left(2x+5\right)=0\Leftrightarrow x=-\frac{5}{2}\)
19 tháng 10 2020
a) x( x + 1 ) - x( x - 5 ) = 6
⇔ x2 + x - x2 + 5x = 6
⇔ 6x = 6
⇔ x = 1
b) 4x2 - 4x + 1 = 0
⇔ ( 2x - 1 )2 = 0
⇔ 2x - 1 = 0
⇔ x = 1/2
c) x2 - 1/4 = 0
⇔ ( x - 1/2 )( x + 1/2 ) = 0
⇔ \(\orbr{\begin{cases}x-\frac{1}{2}=0\\x+\frac{1}{2}=0\end{cases}}\Leftrightarrow x=\pm\frac{1}{2}\)
d) 5x2 = 20x
⇔ 5x2 - 20x = 0
⇔ 5x( x - 4 ) = 0
⇔ \(\orbr{\begin{cases}5x=0\\x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)
e) 4x2 - 9 - x( 2x - 3 ) = 0
⇔ ( 2x - 3 )( 2x + 3 ) - x( 2x - 3 ) = 0
⇔ ( 2x - 3 )( 2x + 3 - x ) = 0
⇔ ( 2x - 3 )( x + 3 ) = 0
⇔ \(\orbr{\begin{cases}2x-3=0\\x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=-3\end{cases}}\)
f) 4x2 - 25 = ( 2x - 5 )( 2x + 7 )
⇔ ( 2x - 5 )( 2x + 5 ) - ( 2x - 5 )( 2x + 7 ) = 0
⇔ ( 2x - 5 )( 2x + 5 - 2x - 7 ) = 0
⇔ ( 2x - 5 )(-2) = 0
⇔ 2x - 5 = 0
⇔ x = 5/2
2
25 tháng 10 2021
\(a,x^2-5x\)
\(=x\left(x-5\right)\)
\(b,5x\left(x+5\right)+4x+20\)
\(=5x\left(x+5\right)+4\left(x+5\right)\)
\(=\left(5x+4\right)\left(x+5\right)\)
\(c,7x\left(2x-1\right)-4x+2\)
\(=7x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(7x-2\right)-\left(2x-1\right)\)
2
25 tháng 10 2021
\(d,x^2-16+2\left(x+4\right)\)
\(=x^2-16+2x+8\)
\(=x\left(x-2\right)-8\) ( Ý này thì k chắc lắm, sai thông cảm :)) )
\(e,x^2-10x+9\)
\(=x^2-x-9x+9\)
\(=x\left(x-1\right)-9\left(x-1\right)\)
\(=\left(x-9\right)\left(x-1\right)\)
\(f,\left(2x-1\right)^2-\left(x-3\right)^2=0\) ( mk đoán bài này là tìm x, sai thì bảo mk để mk sửa nhé )
\(\Rightarrow\left(2x-1\right)^2=\left(x-3\right)^2\)
\(\Leftrightarrow\pm\left(2x-1\right)=\pm\left(x-3\right)\)
\(\Rightarrow\hept{\begin{cases}2x-1=x-3\\-\left(2x-1\right)=-\left(x-3\right)\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x-1-x+3=0\\-2x+1-x+3=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x+2=0\\-3x+4=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=\left(-2\right)\\x=\frac{4}{3}\end{cases}}\)
Vậy ...
LB
1
DN
6 tháng 9 2018
\(a,\left(x-2\right)^2=4x^2+4x+1\)
\(\Rightarrow\left(x-2\right)^2=\left(2x\right)^2+2.x.2+1^2\)
\(\Rightarrow\left(x-2\right)^2=\left(2x+1\right)^2\)
\(\Rightarrow\left(x-2\right)^2-\left(2x+1\right)^2=0\)
\(\Rightarrow\left(x-2-2x-1\right)\left(x-2+2x+1\right)=0\)
\(\Rightarrow\left(-x-3\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}-x-3=0\\3x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-x=3\\3x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy \(x\in\left\{-3;\dfrac{1}{3}\right\}\)
\(b,4x^3-4x^2+9-9x=0\)
\(\Rightarrow4x^2\left(x-1\right)+9\left(1-x\right)=0\)
\(\Rightarrow4x^2\left(x-1\right)+9\left(x-1\right)=0\)
\(\left(4x^2+9\right)\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}4x^2+9=0\\x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}4x^2=-9\\x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2=-\dfrac{3}{2}\\x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\pm\sqrt{-\dfrac{3}{2}}\\x=1\end{matrix}\right.\)
Vậy \(x\in\left\{\sqrt{-\dfrac{3}{2}};-\sqrt{-\dfrac{3}{2}};1\right\}\)
2T
22 tháng 2 2019
\(9x^2-1=\left(3x+1\right)\cdot\left(2x-3\right)\\ \Leftrightarrow\left(3x-1\right)\left(3x+1\right)-\left(3x+1\right)\cdot\left(2x-3\right)=0 \\ \Leftrightarrow\left(3x+1\right)\left[\left(3x-1\right)-\left(2x-3\right)\right]=0\\\Leftrightarrow \left(3x+1\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x+1=0\\x+2=0\end{matrix}\right.\Leftrightarrow}\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=-2\end{matrix}\right.\\ \)
22 tháng 2 2019
1. \(9x^2-1=\left(3x+1\right)\left(2x-3\right)\)
\(\Leftrightarrow\left(3x-1\right)\left(3x+1\right)-\left(3x+1\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\left(3x+1\right)\left(3x-1-2x+3\right)=0\)
\(\Leftrightarrow\left(3x+1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+1=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{3}\\x=-2\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S = \(\left\{\dfrac{-1}{3};-2\right\}\)
2. \(\left(2x-1\right)^2=49\)
\(\Leftrightarrow\left(2x-1\right)^2-7^2=0\)
\(\Leftrightarrow\left(2x-1-7\right)\left(2x-1+7\right)=0\)
\(\Leftrightarrow\left(2x-8\right)\left(2x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-8=0\\2x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=8\\2x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S = \(\left\{4;-3\right\}\)
3. \(\left(5x-3\right)^2-\left(4x-7\right)^2=0\)
\(\Leftrightarrow\left(5x-3-4x+7\right)\left(5x-3+4x-7\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(9x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\9x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{10}{9}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S = \(\left\{-4;\dfrac{10}{9}\right\}\)
4. \(\left(2x+7\right)^2=9\left(x+2\right)^2\)
\(\Leftrightarrow4x^2+28x+49=9\left(x^2+4x+4\right)\)
\(\Leftrightarrow4x^2+28x+49=9x^2+36x+36\)
\(\Leftrightarrow\left(4x^2-9x^2\right)+\left(28x-36x\right)=36-49\)
\(\Leftrightarrow-5x^2-8x=-13\)
\(\Leftrightarrow-5x^2-8x+13=0\)
\(\Leftrightarrow-5x^2+5x-13x+13=0\)
\(\Leftrightarrow-5x\left(x-1\right)-13\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(5x+13\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\5x+13=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-13}{5}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S = \(\left\{1;\dfrac{-13}{5}\right\}\)
27 tháng 6 2018
Mk xin lỗi nha, câu c sai đề
c) (x+6)4 + (x+8)4 = 272
KT
26 tháng 4 2018
a) \(\left(2x+1\right)\left(3x-2\right)=\left(2x+1\right)\left(5x-8\right)\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(3x-2\right)-\left(2x+1\right)\left(5x-8\right)=0\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(3x-2-5x+8\right)=0\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(6-2x\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x+1=0\\6-2x=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=-0,5\\x=3\end{cases}}\)
Vậy...
b) \(ĐKXĐ:\) \(x\ne-2;\) \(x\ne4\)
\(\frac{3}{x+2}+\frac{2}{x-4}=0\)
\(\Leftrightarrow\)\(\frac{3\left(x-4\right)}{\left(x+2\right)\left(x-4\right)}+\frac{2\left(x+2\right)}{\left(x+2\right)\left(x-4\right)}=0\)
\(\Leftrightarrow\)\(\frac{3x-12+2x+4}{\left(x+2\right)\left(x-4\right)}=0\)
\(\Leftrightarrow\)\(\frac{5x-8}{\left(x+2\right)\left(x-4\right)}=0\)
\(\Rightarrow\)\(5x-8=0\)
\(\Leftrightarrow\)\(x=\frac{8}{5}\) (T/m đkxđ)
Vậy...
c) \(x^3+4x^2+4x+3=0\)
\(\Leftrightarrow\)\(x^3+3x^2+x^2+3x+x+3=0\)
\(\Leftrightarrow\)\(x^2\left(x+3\right)+x\left(x+3\right)+\left(x+3\right)=0\)
\(\Leftrightarrow\)\(\left(x+3\right)\left(x^2+x+1\right)=0\)
\(\Leftrightarrow\)\(x+3=0\) (do \(x^2+x+1=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\) \(\forall x\))
\(\Leftrightarrow\)\(x=-3\)
Vậy...
5 tháng 11 2017
\(a,x^4-4x^3+x^2-4x=0\)
\(\Rightarrow\left(x^4-4x^3\right)+\left(x^2-4x\right)=0\)
\(\Rightarrow x^3\left(x-4\right)+x\left(x-4\right)=0\)
\(\Rightarrow\left(x-4\right)\left(x^2+x\right)=0\)
\(\Rightarrow x\left(x-4\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-1\end{matrix}\right.\)
\(b,x^3-5x^2+4x-20=0\)
\(\Rightarrow\left(x^3-5x^2\right)+\left(4x-20\right)=0\)
\(\Rightarrow x^2\left(x-5\right)+4\left(x-5\right)=0\)
\(\Rightarrow\left(x-5\right)\left(x^2+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-5=0\\x^2+4=0\end{matrix}\right.\)
\(\Rightarrow x=5\)
AN
5 tháng 11 2017
a) \(x^4-4x^3+x^2-4x=0\)
\(\Leftrightarrow\left(x^4-4x^3\right)+\left(x^2-4x\right)=0\)
\(\Leftrightarrow x^3\left(x-4\right)+x\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^3+x\right)=0\)
\(\Leftrightarrow x\left(x-4\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x^2+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x^2=-1\left(loai\right)\end{matrix}\right.\)
Vậy x=0; x=4
b) \(x^3-5x^2+4x-20=0\)
\(\Leftrightarrow\left(x^3-5x^2\right)+\left(4x-20\right)=0\)
\(\Leftrightarrow x^2\left(x-5\right)+4\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x^2+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x^2+4=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x^2=-4\left(loai\right)\end{matrix}\right.\)
Vậy x=5
4 tháng 2 2017
a) x3+4x2+x-6=0
<=> x3+x2-2x+3x2+3x-6=0
<=>x(x2+x-2)+3(x2+x-2)=0
<=>(x+3)(x2+x-2)=0
<=>(x+3)(x2+2x-x-2)=0
<=>(x+3)[x(x+2)-(x+2)]=0
<=>(x+3)(x-1)(x+2)=0
=> x+3=0 hay
x-1=0 hay
x+2=0
<=> x=-3 hay x=1 hay x=-2
4 tháng 2 2017
b)x3-3x2+4=0
\(\Leftrightarrow x^3-4x^2+4x+x^2-4x+4=0\)
\(\Leftrightarrow x\left(x^2-4x+4\right)+\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)^2=0\)
\(\Rightarrow\left\{\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left\{\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
(4x^2-9)(x+2)=0
⇔ (4x^2-9)=0 -> (2x-3)(2x+3)=0 -> 2x-3=0 -> x=3/2
2x+3=0 -> x= -3/2
(x+2)=0 -> x=-2
Vậy tập nghiệm S={ 3/2;-3/2;-2}
(4x2-9)(x+2) = 0
<=> [(2x)2 - 32] (x+2) = 0
<=> ( 2x+3)(2x-3)(x+2) = 0
<=> 2x+3 = 0 hoặc 2x-3 = 0 hoặc x+2 = 0
<=> 2x = 0-3 hoặc 2x = 0+3 hoặc x = 0-2
<=> 2x = -3 hoặc 2x = 3 hoặc x = -2
<=> 2x:2 = -3:2 hoặc 2x:2 = 3:2 hoặc x = -2
<=> x = -3/2 hoặc x = 3/2 hoặc x = -2