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7 tháng 6 2017

n) \(\left|3-x\right|+x^2-x\left(x+4\right)=0\)

\(\Rightarrow\left|3-x\right|+x^2-x^2-4x=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3-x-4x=0\left(đk:3-x\ge0\right)\\-\left(3-x\right)-4x=0\left(đk:3-x< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\left(đk:x\le3\right)\\x=-1\left(đk:x>3\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\\x\in\varnothing\end{matrix}\right.\)

Vậy \(x=\dfrac{3}{5}\)

m) \(\left(x-1\right)^2+\left|x+21\right|-x^2-13=0\)

\(\Rightarrow x^2-2x+1+\left|x+21\right|-x^2-13=0\)

\(\Leftrightarrow-2x-12+\left|x+21\right|=0\)

\(\Leftrightarrow\left[{}\begin{matrix}-2x-12+x+21=0\left(đk:x+21\ge0\right)\\-2x-12-\left(x+21\right)=0\left(đk:x+21< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=9\left(đk:x\ge-21\right)\\x=-11\left(đk:x< -21\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=9\\x\in\varnothing\end{matrix}\right.\)

Vậy \(x=9\)

7 tháng 6 2017

e) \(\left|5x\right|=3x-2\)

\(\Rightarrow5\cdot\left|x\right|=3x-2\)

\(\Leftrightarrow5\cdot\left|x\right|-3x=-2\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-3x=-2\left(đk:x\ge0\right)\\5\cdot\left(-x\right)-3x=-2\left(đk:x< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\left(đk:x\ge0\right)\\x=\dfrac{1}{4}\left(đk:x< 0\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x\in\varnothing\end{matrix}\right.\)

Vậy \(x\in\varnothing\)

g) \(\left|-2,5x\right|=x-12\)

\(\Rightarrow2,5\cdot\left|x\right|=x-12\)

\(\Leftrightarrow2x5\cdot\left|x\right|-x=-12\)

\(\Leftrightarrow\left[{}\begin{matrix}2,5x-x=-12\left(đk:x\ge0\right)\\2,5\cdot\left(-x\right)-x=-12\left(đk:x< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-8\left(đk:x\ge0\right)\\x=\dfrac{24}{7}\left(đk:x< 0\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\x\in\varnothing\end{matrix}\right.\)

Vậy \(x\in\varnothing\)

28 tháng 5 2017

a) (x-1)(5x+3)=(3x-8)(x-1)

= (x-1)(5x+3)-(3x-8)(x-1)=0

=(x-1)[(5x+3)-(3x-8)]=0

=(x-1)(5x+3-3x+8)=0

=(x-1)(2x+11)=0

\(\Leftrightarrow\) x-1=0 hoặc 2x+11=0

\(\Leftrightarrow\) x=1 hoặc x=\(\dfrac{-11}{2}\)

Vậy S={1;\(\dfrac{-11}{2}\)}

b) 3x(25x+15)-35(5x+3)=0

=3x.5(5x+3)-35(5x+3)=0

=15x(5x+3)-35(5x+3)=0

=(5x+3)(15x-35)=0

\(\Leftrightarrow\) 5x+3=0 hoặc 15x-35=0

\(\Leftrightarrow\) x=\(\dfrac{-3}{5}\) hoặc x=\(\dfrac{7}{3}\)

Vậy S={\(\dfrac{-3}{5};\dfrac{7}{3}\)}

c) (2-3x)(x+11)=(3x-2)(2-5x)

=(2-3x)(x+11)-(3x-2)(2-5x)=0

=(3x-2)[(x+11)-(2-5x)]=0

=(3x-2)(x+11-2+5x)=0

=(3x-2)(6x+9)=0

\(\Leftrightarrow\) 3x-2=0 hoặc 6x+9=0

\(\Leftrightarrow\) x=\(\dfrac{2}{3}\) hoặc x=\(\dfrac{-3}{2}\)

Vậy S={\(\dfrac{2}{3};\dfrac{-3}{2}\)}

d) (2x2+1)(4x-3)=(2x2+1)(x-12)

=(2x2+1)(4x-3)-(2x2+1)(x-12)=0

=(2x2+1)[(4x-3)-(x-12)=0

=(2x2+1)(4x-3-x+12)=0

=(2x2+1)(3x+9)=0

\(\Leftrightarrow\)2x2+1=0 hoặc 3x+9=0

\(\Leftrightarrow\)x=\(\dfrac{1}{2}\)hoặc x=\(\dfrac{-1}{2}\) hoặc x=-3

Vậy S={\(\dfrac{1}{2};\dfrac{-1}{2};-3\)}

e) (2x-1)2+(2-x)(2x-1)=0

=(2x-1)[(2x-1)+(2-x)=0

=(2x-1)(2x-1+2-x)=0

=(2x-1)(x+1)=0

\(\Leftrightarrow\) 2x-1=0 hoặc x+1=0

\(\Leftrightarrow\) x=\(\dfrac{-1}{2}\) hoặc x=-1

Vậy S={\(\dfrac{-1}{2}\);-1}

f)(x+2)(3-4x)=x2+4x+4

=(x+2)(3-4x)=(x+2)2

=(x+2)(3-4x)-(x+2)2=0

=(x+2)[(3-4x)-(x+2)]=0

=(x+2)(3-4x-x-2)=0

=(x+2)(-5x+1)=0

\(\Leftrightarrow\) x+2=0 hoặc -5x+1=0

\(\Leftrightarrow\) x=-2 hoặc x=\(\dfrac{1}{5}\)

Vậy S={-2;\(\dfrac{1}{5}\)}

11 tháng 1 2018

a ) \(\left(5x+7\right)\left(x-7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{5}\\x=7\end{matrix}\right.\)

b ) \(\left(x^2-1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\\x=-3\end{matrix}\right.\)

c )\(x^2-x-6=0\)

\(\Leftrightarrow x^2-3x+2x-6=0\)

\(\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)

d ) \(x^2+x-12=0\)

\(\Leftrightarrow x^2-4x+3x-12\)

\(\Leftrightarrow\left(x+3\right)\left(x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)

e ) \(15\left(x+9\right)\left(x-3\right)\left(x+21\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-9\\x=3\\x=-21\end{matrix}\right.\)

g ) \(\left(x^2+1\right)\left(x^2+4x+4\right)=0\)

\(\Leftrightarrow\left(x^2+1\right)\left(x+2\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=-1\left(loại\right)\\x=-2\end{matrix}\right.\)

i ) \(x^4+2x^3-2x^2+2x-3=0\)

\(\Leftrightarrow x^4+3x^3-x^3-3x^2+x^2+3x-x-3=0\)

\(\Leftrightarrow x^3\left(x+3\right)-x^2\left(x+3\right)+x\left(x+3\right)-\left(x+3\right)=0\)

\(\Leftrightarrow\left(x^3-x^2+x-1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left(x^2+1\right)\left(x-1\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=-1\left(loại\right)\\x=1\\x=-3\end{matrix}\right.\)

h) \(x^2+5x+6=0\)

\(\Leftrightarrow x^2+3x+2x+6=0\)

\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-3\end{matrix}\right.\)

\(\left(x-5\right)\left(x-1\right)=2x\left(x-1\right)\)

\(\Leftrightarrow\left(x-1\right)\left(x-5-2x\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+5\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-5\end{cases}}\)

Vậy............

\(5\left(x+3\right)\left(x-2\right)-3\left(x+5\right)\left(x+2\right)=0\)

\(\Leftrightarrow5\left(x^2+x-6\right)-3\left(x^2+7x+10\right)=0\)

\(\Leftrightarrow2x^2-16x-60=0\)

\(\Leftrightarrow x^2-8x-30=0\)

làm tiếp nhé!!!!!

25 tháng 2 2018

@Lightning Farron

25 tháng 2 2018

@soyeon_Tiểubàng giải

24 tháng 1 2018

a) đặt \(\left(x^2+x\right)\)là \(y\)

ta có: \(3y^2-7y+4\)\(=0\)

<=>\(\left(3y-4\right)\left(y-1\right)=0\)

còn lại bạn tự xử nhé 

25 tháng 6 2019

a) 2x(x-3)+5(x-3)=0

\(\Leftrightarrow\left(x-3\right)\left(2x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x+5=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\frac{5}{2}\end{matrix}\right.\)

Vậy: phương trình đã cho có tập nghiệm S=\(\left\{3;-\frac{5}{2}\right\}\)