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12 tháng 10 2020
a) 2x (x-5) -(x2-10x +25)=0
\(\Leftrightarrow\)2x(x-5)-(x-5)2=0
\(\Leftrightarrow\)(x-5)(2x-x+5)=0
\(\Leftrightarrow\)(x-5)(x+5)=0
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x-5=0\\x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
b) x2 - 9 +3x(x+3) = 0
\(\Leftrightarrow\)(x2 - 9) +3x(x+3) =0
\(\Leftrightarrow\)(x-3)(x+3)+3x(x+3)=0
\(\Leftrightarrow\)(x+3)(x-3+3x)=0
\(\Leftrightarrow\)(x+3)(4x-3)=0
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x+3=0\\4x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=-3\\4x=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\frac{3}{4}\end{matrix}\right.\)
c) x3 - 16x = 0
\(\Leftrightarrow\)x(x2-16)=0
\(\Leftrightarrow\)x(x-4)(x+4)=0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
d) (2x+3)(x-2) - (x2 -4x+4) = 0
\(\Leftrightarrow\)(2x+3)(x-2) -(x-2)2=0
\(\Leftrightarrow\)(x-2)(2x+3-x+2)=0
\(\Leftrightarrow\)(x-2)(x+5)=0
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
e) 9x2 -(x2 -2x +1)=0
\(\Leftrightarrow\)(3x)2-(x-1)2=0
\(\Leftrightarrow\)(3x-x+1)(3x+x-1)=0
\(\Leftrightarrow\)(2x+1)(4x-1)=0
\(\Leftrightarrow\)\(\left[{}\begin{matrix}2x+1=0\\4x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}2x=-1\\4x=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{-1}{2}\\x=\frac{1}{4}\end{matrix}\right.\)
f)x3-4x2 -9x +36 = 0
\(\Leftrightarrow\)(x3-9x)-(4x2-36)=0
\(\Leftrightarrow\)x(x2-9)-4(x2-9)=0
\(\Leftrightarrow\)(x-4)(x2-9)=0
\(\Leftrightarrow\)(x-4)(x-3)(x+3)=0
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-3=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=4\\x=3\\x=-3\end{matrix}\right.\)
g) 3x - 6 = (x-1).(x-2)
\(\Leftrightarrow\)3(x-2)=(x-1)(x-2)
\(\Leftrightarrow\)x-1=3
\(\Leftrightarrow\)x=4
i) (x-2).(x+2) +(2x+1)2 =-5x.(x-3) =5 (?? đề sao vậy ??)
k) x2 -1 = (x-1).(2x+3)
\(\Leftrightarrow\)(x-1)(x+1)=(x-1)(2x+3)
\(\Leftrightarrow\)x+1=2x+3
\(\Leftrightarrow\)x-2x=3-1
\(\Leftrightarrow\)-x=2
\(\Leftrightarrow\)x=-2
l) (2x-1)2 +(x+3).(x-3) -5x(x-2)=6
\(\Leftrightarrow\)4x2-4x+1+x2-9-5x2+10x=6
\(\Leftrightarrow\)6x-8=6
\(\Leftrightarrow\)6x=14
\(\Leftrightarrow\)x=\(\frac{7}{3}\)
NV
Nguyễn Việt Lâm
Giáo viên
7 tháng 9 2020
a/
\(\Leftrightarrow x-2x^2+2x^2-3x-4x+6=0\)
\(\Leftrightarrow-6x+6=0\)
\(\Leftrightarrow x=1\)
b/
\(\Leftrightarrow2x^2-4x-2x^2-6x=0\)
\(\Leftrightarrow-10x=0\)
\(\Leftrightarrow x=0\)
c/
\(\Leftrightarrow\left(2x+3\right)\left(2x+3+x-3\right)=0\)
\(\Leftrightarrow3x\left(2x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\frac{3}{2}\end{matrix}\right.\)
NV
Nguyễn Việt Lâm
Giáo viên
7 tháng 9 2020
c/
\(\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(9y^2+30y+25\right)=0\)
\(\Leftrightarrow\left(x-y\right)^2+\left(3y+5\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\3x+5=0\end{matrix}\right.\)
\(\Leftrightarrow x=y=-\frac{5}{3}\)
d/
\(\Leftrightarrow4x^2-4x+1+4x^2+4x+1-2\left(4x^2-2x-2\right)+x=12\)
\(\Leftrightarrow8x^2+x+2-8x^2+4x+4=12\)
\(\Leftrightarrow5x=6\)
\(\Leftrightarrow x=\frac{6}{5}\)
22 tháng 8 2017
a)\(x^2+3x+6=x^2+2.\frac{3}{2}x+\frac{9}{4}+\frac{15}{4}=0\)
\(\left(x+\frac{3}{2}\right)^2+\frac{15}{4}=0\)
\(\left(x+\frac{3}{2}\right)^2=-\frac{15}{4}\)
Vì bình phương luôn lớn hơn hoặc bằng 0
Nên PT vô nghiệm
b)\(x^2-2x-3=0\)
\(x^2-3x+x-3=0\)
\(\left(x+1\right)\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+1=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=3\end{cases}}\)
22 tháng 8 2017
d)\(x^3-2x^2-x+2=0\)
\(x^2\left(x-2\right)-\left(x-2\right)=0\)
\(\left(x-1\right)\left(x+1\right)\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x+1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
x - 2 = 0 x=2
c)\(2x^2+7x+3=0\)
\(2x^2+x+6x+3=0\)
\(x\left(2x+1\right)+3\left(2x+1\right)=0\)
\(\left(2x+1\right)\left(x+3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x+1=0\\x+3=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{1}{2}\\x=-3\end{cases}}\)
31 tháng 12 2017
a. \(2x\left(x+5\right)-x\left(3+2x\right)=26\Leftrightarrow2x^2+10x-3x-2x^2=26\Leftrightarrow7x=26\Leftrightarrow x=\dfrac{26}{7}\)
Vậy \(x=\dfrac{26}{7}\)
b. \(5x\left(x-1\right)=x-1\Leftrightarrow5x\left(x-1\right)-\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(5x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x-1=0\\5x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\5x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\)
c. \(2\left(x+5\right)-x^2-5x=0\Leftrightarrow2\left(x+5\right)-x\left(x+5\right)=0\Leftrightarrow\left(x+5\right)\left(2-x\right)=0\Leftrightarrow\left[{}\begin{matrix}x+5=0\\2-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
d. \(\left(2x-3\right)^2-\left(x+5\right)^2=0\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\Leftrightarrow\left(x-8\right)\left(3x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x-8=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\3x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
e. \(3x^3-48x=0\Leftrightarrow3x\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}3x=0\\x^2-16=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm4\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=0\\x=\pm4\end{matrix}\right.\)
f. \(x^3+x^2-4x=4\Leftrightarrow x^3+x^2-4x-4=0\Leftrightarrow\left(x^2-4x+4\right)+\left(x^3-8\right)=0\Leftrightarrow\left(x-2\right)^2+\left(x-2\right)\left(x^2+2x+4\right)=0\Leftrightarrow\left(x-2\right)\left(x-2+x^2+2x+4\right)=0\left(x-2\right)\left(x^2+3x+2\right)=0\Leftrightarrow\left(x-2\right)\left(x^2+x+2x+2\right)=0\Leftrightarrow\left(x-2\right)\left[x\left(x+1\right)+2\left(x+1\right)\right]=0\Leftrightarrow\left(x-2\right)\left(x+1\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\\x=-2\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-1\\x=\pm2\end{matrix}\right.\)
g. \(\left(x-1\right)\left(2x+3\right)-x\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(2x+3-x\right)=0\Leftrightarrow\left(x-1\right)\left(x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
h. \(x^2-4x+8=2x-1\Leftrightarrow x^2-4x+8-2x+1=0\Leftrightarrow x^2-6x+9=0\Leftrightarrow\left(x-3\right)^2=0\Leftrightarrow x-3=0\Leftrightarrow x=3\)
Vậy \(x=3\)
__________________________Chúc bạn học tốt____________________________
DH
1
20 tháng 4 2020
a) Ta có: \(\left(2x-4\right)\left(3x+1\right)+\left(x-2\right)^2=0\)
\(\Leftrightarrow\left(x-2\right)\left[2\left(3x+1\right)+\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(6x+2+x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\cdot7x=0\)
Vì 7≠0
nên \(\left[{}\begin{matrix}x-2=0\\x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)
Vậy: x∈{0;2}
b) Ta có: \(\left(2x+1\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\cdot3x=0\)
Vì 3≠0
nên \(\left[{}\begin{matrix}x+2=0\\x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right.\)
Vậy: x∈{0;-2}
c) Ta có: \(2x^2-x=0\)
\(\Leftrightarrow x\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\2x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{1}{2}\end{matrix}\right.\)
Vậy: \(x\in\left\{0;\frac{1}{2}\right\}\)
d) Ta có: \(x^3-6x^2+9x=0\)
\(\Leftrightarrow x\left(x^2-6x+9\right)=0\)
\(\Leftrightarrow x\left(x-3\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x-3\right)^2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
Vậy: x∈{0;3}
k) Ta có: \(x^3+3x^2+x+3=0\)
\(\Leftrightarrow x^2\left(x+3\right)+\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2+1\right)=0\)(1)
Ta có: \(x^2+1\ge1>0\forall x\)(2)
Từ (1) và (2) suy ra x+3=0
hay x=-3
Vậy: x=-3
17 tháng 4 2023
cái bài a) thì số 2 đâu ra thế bạn?
<=>(x−2)[2(3x+1)+(x−2)]=0
CM
4 tháng 12 2018
a) \(2x\left(x-3\right)+5\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(2x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\2x+5=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\2x=-5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\)
b) \(\left(x^2-4\right)-\left(x-2\right)\left(3-2x\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2\right)-\left(x-2\right)\left(3-2x\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2-3+2x\right)=0\)
\(\Rightarrow\left(x-2\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\3x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\3x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)
c) \(\left(2x+5\right)^2=\left(x+2\right)^2\)
\(\Rightarrow\left(2x+5\right)^2-\left(x+2\right)^2=0\)
\(\Rightarrow\left(2x+5-x-2\right)\left(2x+5+x+2\right)=0\)
\(\Rightarrow\left(x+3\right)\left(3x+7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+3=0\\3x+7=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\3x=-7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=-\dfrac{7}{3}\end{matrix}\right.\)
d) \(x^2-5x+6=0\)
\(\Rightarrow x^2-2x-3x+6=0\)
\(\Rightarrow x\left(x-2\right)-3\left(x-2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
e) \(2x^3+6x^2=x^2+3x\)
\(\Rightarrow2x^3+6x^2-x^2-3x=0\)
\(\Rightarrow2x^3+5x^2-3x=0\)
\(\Rightarrow x\left(2x^2+5x-3\right)=0\)
\(\Rightarrow2x^2+5x-3=0\)
\(\Rightarrow2x^2-6x+x-3=0\)
\(\Rightarrow2x\left(x-3\right)+\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)\left(2x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\2x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{2}\end{matrix}\right.\)
f) \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)-2x^2\)
\(\Rightarrow\left(x^2-1\right)\left(x+2\right)-\left(x^3-8\right)-2x^2=0\)
\(\Rightarrow x^3+2x^2-x+2-x^3+8-2x^2=0\)
\(\Rightarrow-x+10=0\)
\(\Rightarrow x=10\)
HP
14 tháng 8 2016
a) \(\left(y-1\right)^2=9\)
\(\Rightarrow\left(y-1\right)^2=3^2=\left(-3\right)^2\)
\(\Rightarrow x-1=3\Rightarrow x=4\)
\(\Rightarrow x-1=-3\Rightarrow x=-2\)
Vậy: \(x=4\) hoặc \(-2\)
NQ
3
KY
14 tháng 9 2019
a) \(x^3+2x^2+2x+1=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2+x+1\right)=0\)
\(TH1:x+1=0\Leftrightarrow x=-1\)
\(TH2:x^2+x+1=0\)
\(\Leftrightarrow\left(x+\frac{1}{2}\right)^2+\frac{3}{4}=0\)
Mà \(\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)nên loại TH2
Vậy x = 1
KY
14 tháng 9 2019
Câu a), x = -1 nha, kết luận nhầm
b) \(x^3-4x^2+12x-27=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-3x+9\right)-4x\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-7x+9\right)=0\)
\(TH1:x-3=0\Leftrightarrow x=3\)
\(TH2:x^2-7x+9=0\)
\(\cdot\Delta=\left(-7\right)^2-4.9=13\)
Vậy pt của TH2 có 2 nghiệm phân biệt
\(x_1=\frac{7+\sqrt{13}}{2}\);\(x_2=\frac{7-\sqrt{13}}{2}\)
13 tháng 7 2018
Mình giải từ cuối lên , mình giải dần -)
n, <=> x(2x-1)-3(2x-1)=0
<=> (x-3)(2x-1)=0
<=> x= 3 hoặc x= 1/2
m, <=> (x+2)(x2-3x+5)-x2(x+2)=0
<=> (x+2)(x2-3x+5-x2)=0
<=> (x+2)(5-3x)=0
=> x= -2 hoặc5/3
TN
17 tháng 6 2017
\(a,x^4-16x^2+32x-16=0\)
\(\Leftrightarrow\left(x^4-16\right)-16x\left(x-2\right)=0\)
\(\Leftrightarrow\left(x^4+4\right)\left(x-2\right)\left(x+2\right)-16x\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3+2x^2-12x+8\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-2x^2+4x^2-8x-4x+8\right)=0\)\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x-2\right)+4x\left(x-2\right)-4\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-2\right)\left(x^2+4x-4\right)=0\)
\(\Leftrightarrow\left(x-2\right)^2\left[\left(x+2\right)^2-8\right]=0\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^2=0\\\left(x+2\right)^2-8=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x+2\right)^2=8\Rightarrow\left[{}\begin{matrix}x+2=\sqrt{8}\\x+2=-\sqrt{8}\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\sqrt{8}-2\\x=-\sqrt{8}-2\end{matrix}\right.\)
2x3 - x2 + x + 1 = 0
<=> 2x3 + 2 - x2 + x - 1 = 0
<=> 2(x3 + 1) - (x2 - x + 1) = 0
<=> 2(x + 1)(x2 - x + 1) - (x2 - x + 1) = 0
<=> (x2 - x + 1)[2(x + 1) - 1)] = 0
<=> (x2 - x + 1)(2x + 1) = 0
<=> 2x + 1 = 0 (Vì x2 - x + 1 > 0 \(\forall x\inℝ\))
<=> x = -1/2
Vậy x = -1/2 là nghiệm phương trình