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15 tháng 12 2014

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

<=>(2x-3-x-5)(2x-3+x+5)=0

<=>(x-8)(3x+2)=0

<=>x-8=0 hoặc 3x+2=0

<=>x=8 hoặc x=-2/3


 

7 tháng 12 2017

(2x-3)2
-(x+5)2=0
<=>(2x-3-x-5)(2x-3+x+5)=0
<=>(x-8)(3x+2)=0
<=>x-8=0 hoặc 3x+2=0
<=>x=8 hoặc x=-2/3

chcú cậu hok tốt @_@

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____________________________

1 tháng 1 2018

Thankshihi

3 tháng 8 2019

\(x\left(2x-7\right)-4x+14=0\Leftrightarrow\left(x-2\right)\left(2x-7\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\2x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{7}{2}\end{matrix}\right.\)

\(x^2\left(x-1\right)-4\left(x-1\right)=\left(x^2-4\right)\left(x-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=1\end{matrix}\right.\)

\(x^4-x^3-x^2+x=x\left(x^3+1\right)-x^2\left(x+1\right)=x\left(x+1\right)\left(x^2-x+1-x^2\right)=x\left(x+1\right)\left(1-x\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\\1-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm1\end{matrix}\right.\)

a) \(x\left(2x-7\right)-4x+14-0\Leftrightarrow2x^2-11x+14=0\Leftrightarrow2x^2-4x-7x+14=0\Leftrightarrow2x\left(x-2\right)-7\left(x-2\right)=0\Leftrightarrow\left(2x-7\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=3,5\\x=2\end{matrix}\right.\)

b) \(x^2\left(x-1\right)-4x+4=0\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-2\end{matrix}\right.\)

c) \(x+x^2-x^3-x^4=0\Leftrightarrow x\left(x^3+x^2-x-1\right)=0\Leftrightarrow x\left[x\left(x^2-1\right)+\left(x^2-1\right)\right]=0\Leftrightarrow x\left(x+1\right)\left(x^2-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)

d) \(2x^3+3x^2+2x+3=0\Leftrightarrow x^2\left(2x+3\right)+2x+3=0\Leftrightarrow\left(x^2+1\right)\left(2x+3\right)=0\Leftrightarrow x=-1,5\left(x^2+1>0\forall x\right)\)

e) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\Leftrightarrow\left(2x-5\right)\left(2x+5\right)-\left(2x-5\right)\left(2x+7\right)=0\Leftrightarrow\left(2x-5\right)\left(2x+5-2x-7\right)=0\Leftrightarrow2x-5=0\Leftrightarrow x=2,5\)

g) \(x^3+27+\left(x+3\right)\left(x-9\right)=0\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\Leftrightarrow x\left(x+3\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=2\end{matrix}\right.\)

26 tháng 8 2019

a) \(3x^3-6x^2=0\)

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

\(\orbr{\begin{cases}3x^2=0\\x-2=0\end{cases}}\)

\(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

b) \(x\left(x-4\right)-12x+48=0\)

\(x^2-4x-12x+48=0\)

\(x^2-16x+48=0\)

\(\left(x-12\right)\left(x-4\right)=0\)

\(\orbr{\begin{cases}x-12=0\\x-4=0\end{cases}}\)

\(\orbr{\begin{cases}x=12\\x=4\end{cases}}\)

c) Viết thiếu nha :v

d) \(2x\left(x-5\right)-x\left(2x+3\right)=16\)

\(2x^2-10x-x^2-2x^2-3x=16\)

\(-13x=16\)

\(x=-\frac{16}{13}\)

e) \(\left(4x^2-1\right)-\left(x-1\right)^2=-3\)

\(4x^2-1-x^2+2x-1=-3\)

\(3x^2-2+2x=-3\)

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

\(3x^2+1+2x=0\)

Vì \(3x^2+1+2x>0\)nên: 

\(x\in\varnothing\)

26 tháng 8 2019

A) 3x3 - 6x2 = 0

=> 3x2(x - 2) = 0

=> \(\orbr{\begin{cases}3x^2=0\\x-2=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

b) x(x - 4) - 12x + 48 = 0

=> x(x - 4) - 12(x - 4) = 0

=> (x - 12)(x - 4) = 0

=> \(\orbr{\begin{cases}x-12=0\\x-4=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=12\\x=4\end{cases}}\)

c) x(x - 4) - (x2 - 8) = x2 - 4x - x2 + 8 = 4x + 8 

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

13 tháng 7 2018

trả lời chi tiết giúp mình với

18 tháng 9 2018

Bài 1:

a) \(9\left(4x+3\right)^2=16\left(3x-5\right)^2\)

\(114x^2+216x+81=114x^2-480x+400\)

\(144x^2+216x=144x^2-480x+400-81\)

\(114x^2+216=114x^2-480x+319\)

\(696x=319\)

\(\Rightarrow x=\frac{11}{24}\)

b) \(\left(x^3-x^2\right)^2-4x^2+8x-4=0\)

\(\left(x-1\right)^2\left(x^2+2\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)=0\)

\(\Rightarrow x=1\)

c) \(x^5+x^4+x^3+x^2+x+1=0\)

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

\(\Rightarrow x=-1\)

Bài 2:

a) \(5x^3-7x^2-15x+21=0\)

\(\left(5x-7\right)\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)=0\)

\(\Rightarrow x=\frac{7}{5}\)

b) \(\left(x-3\right)^2=4x^2-20x+25\)

\(x^2-6x+9-25=4x^2-20x+25\)

\(x^2-6x+9=4x^2-20x+25-25\)

\(x^2-6x-16=4x^2-20x\)

\(x^2+14x-16=4x^2-4x^2\)

\(-3x^2+14x-16=0\)

\(\Rightarrow\orbr{\begin{cases}x=2\\x=\frac{8}{3}\end{cases}}\)

c) \(\left(x-1\right)^2-5=\left(x+2\right)\left(x-2\right)-x\left(x-1\right)\)

\(x^2-2x=x-4\)

\(x^2-2x=x-4+4\)

\(x^2-2x=x-x\)

\(x^2-3x=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)

d) \(\left(2x-3\right)^3-\left(2x+3\right)\left(4x^2-1\right)=-24\)

\(-48x^2+56x-24=-24\)

\(-48x^2+56x=-24+24\)

\(-48x^2+56=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{7}{6}\end{cases}}\)

mình ko chắc

Bài 1

A, 11/24

B, -1

chúc bn học tốt

12 tháng 7 2019

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

\(\Leftrightarrow\left(2x-1+2x+4\right)\left(2x-1-2x-4\right)=0\)

\(\Leftrightarrow-5\left(4x+3\right)=0\)

\(\Leftrightarrow4x+3=0\)

\(\Leftrightarrow4x=-3\)

\(\Leftrightarrow x=\frac{-3}{4}\)

Vậy tập nghiệm của pt là \(S=\left\{\frac{-3}{4}\right\}\)

12 tháng 7 2019

h) \(\left(2x-3\right)\left(3x+1\right)-x\left(6x+10\right)=30\)

\(\Leftrightarrow3x\left(2x-3\right)+\left(2x-3\right)-6x^2-10x=30\)

\(\Leftrightarrow6x^2-9x+2x-3-6x^2-10x=30\)

\(\Leftrightarrow-9x+2x-3-10x=30\)

\(\Leftrightarrow-17x-3=30\)

\(\Leftrightarrow-17x=33\)

\(\Leftrightarrow x=\frac{-33}{17}\)

Vậy tập nghiệm của pt là \(S=\left\{\frac{-33}{17}\right\}\)

6 tháng 10 2020

a) \(4x^3-9x=0\)

\(\Leftrightarrow x\left(4x^2-9\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\4x^2=9\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm\frac{3}{2}\end{cases}}\)

b) \(3x\left(x-2\right)-5x+10=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=2\end{cases}}\)

c) \(4x\left(x+3\right)-x^2+9=0\)

\(\Leftrightarrow4x\left(x+3\right)-\left(x-3\right)\left(x+3\right)=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-3\end{cases}}\)

d) \(\left(2x+5\right)\left(x-4\right)=\left(x-4\right)\left(5-x\right)\)

\(\Leftrightarrow\left(2x+5\right)\left(x-4\right)+\left(x-5\right)\left(x-4\right)=0\)

\(\Leftrightarrow3x\left(x-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)

6 tháng 10 2020

e) \(16x^2-25=\left(4x-5\right)\left(2x+1\right)\)

\(\Leftrightarrow\left(4x-5\right)\left(4x+5\right)-\left(4x-5\right)\left(2x+1\right)=0\)

\(\Leftrightarrow\left(4x-5\right)\left(2x+4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{4}\\x=-2\end{cases}}\)

f) \(\left(x+\frac{1}{5}\right)^2=\frac{64}{9}\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{5}=\frac{8}{3}\\x+\frac{1}{5}=-\frac{8}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{37}{15}\\x=-\frac{43}{15}\end{cases}}\)

g) \(9\left(x+2\right)^2=\left(x+3\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}3x+6=x+3\\3x+6=-x-3\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=-3\\4x=-9\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{2}\\x=-\frac{9}{4}\end{cases}}\)