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C
1
NV
Nguyễn Việt Lâm
Giáo viên
20 tháng 7 2021
a.
\(\Leftrightarrow\left(3x-1\right)^3=\left(-\dfrac{1}{2}\right)^3\)
\(\Leftrightarrow3x-1=-\dfrac{1}{2}\)
\(\Leftrightarrow3x=\dfrac{1}{2}\)
\(\Leftrightarrow x=\dfrac{1}{6}\)
b.
\(\Leftrightarrow\left(2x-1\right)\left(x-4\right)-x\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(2x-1-x\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{2}\\\end{matrix}\right.\)
c.
\(\Leftrightarrow3x\left(5x-2\right)-2\left(5x-2\right)=0\)
\(\Leftrightarrow\left(3x-2\right)\left(5x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{2}{5}\end{matrix}\right.\)
2T
16 tháng 8 2019
d) \(4x^2-9-x\left(2x-3\right)=0\)
\(\Leftrightarrow4x^2-9-2x^2+3x=0\)
\(\Leftrightarrow2x^2+3x-9=0\)
\(\Delta=3^2-4.2.\left(-9\right)=9+72=81\)
Vậy pt có 2 nghiệm phân biệt
\(x_1=\frac{-3+\sqrt{81}}{4}=\frac{-3}{2}\);\(x_1=\frac{-3-\sqrt{81}}{4}=-3\)
2T
16 tháng 8 2019
e) \(x^3+5x^2+9x=-45\)
\(\Leftrightarrow x^3+5x^2+9x+45=0\)
\(\Leftrightarrow x^2\left(x+5\right)+9\left(x+5\right)=0\)
\(\Leftrightarrow\left(x^2+9\right)\left(x+5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2+9=0\\x+5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm3i\\x=-5\end{cases}}\)
16 tháng 10 2020
Bài 1: Tìm x
a) Ta có: \(\left(2x+1\right)^2-4\left(x+2\right)^2=9\)
\(\Leftrightarrow4x^2+4x+1-4\left(x^2+4x+4\right)-9=0\)
\(\Leftrightarrow4x^2+4x+1-4x^2-16x-16-9=0\)
\(\Leftrightarrow-12x-24=0\)
\(\Leftrightarrow-12x=24\)
hay x=-2
Vậy: x=-2
b) Ta có: \(\left(3x-1\right)^2+2\left(x+3\right)^2+11\left(x+1\right)\left(1-x\right)=6\)
\(\Leftrightarrow9x^2-6x+1+2\left(x^2+6x+9\right)-11\left(x-1\right)\left(x+1\right)-6=0\)
\(\Leftrightarrow9x^2-6x+1+2x^2+12x+18-11\left(x^2-1\right)-6=0\)
\(\Leftrightarrow11x^2+6x+12-11x^2+11=0\)
\(\Leftrightarrow6x+23=0\)
\(\Leftrightarrow6x=-23\)
hay \(x=-\frac{23}{6}\)
Vậy: \(x=-\frac{23}{6}\)
c) Ta có: \(8x^3-12x^2+6x-1=0\)
\(\Leftrightarrow\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3=0\)
\(\Leftrightarrow\left(2x-1\right)^3=0\)
\(\Leftrightarrow2x-1=0\)
\(\Leftrightarrow2x=1\)
hay \(x=\frac{1}{2}\)
Vậy: \(x=\frac{1}{2}\)
d) Ta có: \(x^3+9x^2+27x+27=0\)
\(\Leftrightarrow x^3+3\cdot x^2\cdot3+3\cdot x\cdot3^2+3^3=0\)
\(\Leftrightarrow\left(x+3\right)^3=0\)
\(\Leftrightarrow x+3=0\)
hay x=-3
Vậy: x=-3
KV
16 tháng 10 2020
a) (2x + 1)2 - 4(x + 2)2 = 9
4x2 + 4x + 1 - 4(x2 + 4x + 4) = 9
4x2 + 4x + 1 - 4x2 - 16x - 16 = 9
-12x - 15 = 9
-12x = 9 + 15
-12x = 24
x = 12 : (-2)
x = -2
b) (3x - 1)2 + 2(x + 3)2 + 11(x + 1)(1 - x) = 6
9x2 - 6x + 1 + 2(x2 + 6x + 9) - 11(x + 1)(x - 1) = 6
9x2 - 6x + 1 + 2x2 + 12x + 18 - 11(x2 - 1) = 6
9x2 - 6x + 1 + 2x2 + 12x + 18 - 11x2 + 11 = 6
6x + 30 = 6
6x = 6 - 30
6x = -24
x = -24 : 6
x = -4
c) 8x3 - 12x2 + 6x - 1 = 0
(2x)3 - 3.(2x)2.1 + 3.2x.12 - 13 = 0
(2x - 1)3 = 0
2x - 1 = 0
2x = 1
x = 1/2
d) x3 + 9x2 + 27x + 27 = 0
x3 + 3.x2.3 + 3.x.32 + 33 = 0
(x + 3)3 = 0
x + 3 = 0
x = 0 - 3
x = -3
PQ
2
16 tháng 4 2017
a) -3x(2x-5)-2x(2-3x)=7
=> -6x2 + 15 - 4x + 6x2 = 7
=> -6x2 + 6x2 + 15 -4x =7
=> 15 - 4x =7
=> 4x = 15-7 =8
=> x= 8:4 = 2
b) \(\left(9x-12x+4\right)\left(2-5x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}9x-12x+4=0\\2-5x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x\left(9-12\right)=-4\\5x=2\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}-3x=-4\\x=\frac{2}{5}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=\frac{2}{5}\end{cases}}\)
Vay...
c) (4-3x) = (5+2x)
=> 4-3x=5+2x
=> -3x - 2x = 5-4
=> x(-3-2) = 1
=> -5x = 1
=> x= \(\frac{-1}{5}\)
d) (2x-1)-3(2x-1)=0
=> 2x-1 - 6x + 3 =0
=> 2x - 6x = 1 -3
=> x(2-6)=-2
=> -4x= -2
=> x = \(\frac{1}{2}\)
LT
16 tháng 4 2017
d)(2x-1)-3(2x-1)
=>1(2x-1)-3(2x-1)=0
=>(1-3).(2x-1)=0
=>-2(2x-1)=0
=>2x-1=0
=>2x=-1
=>x=-0,5
vay x =-0,5
VD
2
27 tháng 10 2021
a: \(9x^2-30x+25=0\)
\(\Leftrightarrow3x-5=0\)
hay \(x=\dfrac{5}{3}\)
c: \(9x^2-25=0\)
\(\Leftrightarrow\left(3x-5\right)\left(3x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-\dfrac{5}{3}\end{matrix}\right.\)
27 tháng 10 2021
a) \(9x^2-30x+25=0\Rightarrow\left(3x-5\right)^2=0\Rightarrow x=\dfrac{5}{3}\)
b) \(25x^2-5x+\dfrac{1}{4}=0\Rightarrow\left(10x-1\right)^2=0\Rightarrow x=\dfrac{1}{10}\)
c) \(9x^2-25=0\Rightarrow\left(3x-5\right)\left(3x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-\dfrac{5}{3}\end{matrix}\right.\)
d) \(\left(2x-1\right)^2-\left(3x+2\right)^2=0\)
\(\Rightarrow\left(2x-1+3x+2\right)\left(2x-1-3x-2\right)=0\)
\(\Rightarrow-\left(5x+1\right)\left(5x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{5}\\x=-\dfrac{3}{5}\end{matrix}\right.\)
R
9 tháng 7 2019
Bài 1:tìm x ,biết:
a) (2x - 1)(3x + 2) - 6x(x + 1) = 0
\(\Leftrightarrow6x^2+x-2-6x^2-6x=0\)
\(\Leftrightarrow-5x=2\)
\(\Leftrightarrow x=\frac{-2}{5}\)
b) \(\left(4x-1\right)^2-\left(2x+1\right)\left(8x-3\right)=0\)
\(\Leftrightarrow16x^2-8x+1-16x^2-2x+3=0\)
\(\Leftrightarrow-10x=-4\)
\(\Leftrightarrow x=\frac{2}{5}\)
c) \(4x^2-1=2\left(2x+1\right)\)
\(\Leftrightarrow\left(2x+1\right)\left(2x-1\right)-2\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{3}{2}\end{cases}}\)
2a) \(4x^2-9y^2-6y-1=4x^2-\left(3y+1\right)^2\)
\(=\left(2x-3y-1\right)\left(2x+3y+1\right)\)
b) \(4x^2-1-2x\left(2x-1\right)=\left(2x-1\right)\left(2x+1\right)-2x\left(2x-1\right)\)
\(=1.\left(2x-1\right)\)
c) \(x^2-8x-4y^2+16=\left(x-4\right)^2-4y^2\)
\(=\left(x-4-2y\right)\left(x-4+2y\right)\)
d) \(9x^2-12x-y^2+4=\left(3x-2\right)^2-y^2\)
\(=\left(3x-2-y\right)\left(3x-2+y\right)\)
e) \(4x^2+10x-5=4x^2+2.2.\frac{5}{2}x+\frac{25}{4}-\frac{25}{4}-5\)
\(=\left(2x+\frac{5}{2}\right)^2-\frac{45}{4}\)
\(=\left(2x+\frac{5+3\sqrt{5}}{2}\right)\left(2x+\frac{5-3\sqrt{5}}{2}\right)\)
C
1
7 tháng 7 2021
\(a,\left(3x-7\right)^2=\left(2-2x\right)^2\)
a,\(=>\left(3x-7\right)^2-\left(2-2x\right)^2=0\)
\(< =>\left(3x-7+2-2x\right)\left(3x-7-2+2x\right)=0\)
\(< =>\left(x-5\right)\left(5x-9\right)=0=>\left[{}\begin{matrix}x=5\\x=1,8\end{matrix}\right.\)
b, \(x^2-8x+6=0< =>x^2-2.4x+16-10=0\)
\(< =>\left(x-4\right)^2-\sqrt{10}^2=0\)
\(=>\left(x-4+\sqrt{10}\right)\left(x-4-\sqrt{10}\right)=0\)
\(=>\left[{}\begin{matrix}x=4-\sqrt{10}\\x=4+\sqrt{10}\end{matrix}\right.\)
c, \(4x^2-2x-1=0\)
\(< =>\left(2x\right)^2-2.2.\dfrac{1}{2}x+\dfrac{1}{4}-\dfrac{5}{4}=0\)
\(=>\left(2x-\dfrac{1}{2}\right)^2-\left(\dfrac{\sqrt{5}}{2}\right)^2=0\)
\(=>\left(2x+\dfrac{-1+\sqrt{5}}{2}\right)\left(2x-\dfrac{1+\sqrt{5}}{2}\right)=0\)
\(=>\left[{}\begin{matrix}x=\dfrac{1-\sqrt{5}}{4}\\x=\dfrac{1+\sqrt{5}}{4}\end{matrix}\right.\)
d,\(x^4-4x^2-32=0\)
đặt \(t=x^2\left(t\ge0\right)=>t^2-4t-32=0\)
\(< =>t^2-2.2t+4-6^2=0\)
\(=>\left(t-2\right)^2-6^2=0=>\left(t-8\right)\left(t+4\right)=0\)
\(=>\left[{}\begin{matrix}t=8\left(tm\right)\\t=-4\left(loai\right)\end{matrix}\right.\)\(=>x=\pm\sqrt{8}\)
Ta có : 12x2 + 8x = 0
<=> 4x(3x + 2) = 0
\(\Leftrightarrow\orbr{\begin{cases}4x=0\\3x+2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\3x=-2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\frac{2}{3}\end{cases}}\)
a, 4x(3x - 2) = 0
=> x=0 hoac x= 2/3
b, 2x2 + 10x - x -5 =0
<=> (x + 5)(2x-1) =0
=> x = -5 hoac x = 1/2