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4 tháng 4 2020

a) (x^5 + 4x^3 - 6x^2) : 4x^2

= (x^5 : 4x^2) + (4x^3 : 4x^2) - (6x^2 : 4x^2)

= 1/4x^3 + x + 3/2

b) x(2x^2 - 3) - x^2(5x + 1) + x^2

= 2x^3 - 3x - 5x^3 - x^2 + x^2

= -3x^3 - 3x

c) (x - 2)^2 - (x - 1)(x + 1) - x(1 - x)

= x^2 - 4x + 4 - x^2 + 1 - x + x^2

<=> x^2 - 5x + 5

d) 1/2x^2(6x - 3) - x(x^2 + 1/2) + 1/2(x + 4)

\(\frac{x^2}{2}\left(6x-3\right)-x\left(x^2+\frac{1}{2}\right)+\frac{x+4}{2}\)

\(\frac{x^2\left(6x-3\right)}{2}-x\left(x^2+\frac{1}{2}\right)+\frac{x+4}{2}\)

\(-x\left(x^2+\frac{1}{2}\right)+\frac{x^2\left(6x-3\right)+x+4}{2}\)

\(\frac{4x^3-3x^2+4}{2}\)

22 tháng 4 2020

d, (x2 + 4x + 8)2 + 3x(x2 + 4x + 8) + 2x2 = 0

Đặt x2 + 4x + 8 = t ta được:

t2 + 3xt + 2x2 = 0

\(\Leftrightarrow\) t2 + xt + 2xt + 2x2 = 0

\(\Leftrightarrow\) t(t + x) + 2x(t + x) = 0

\(\Leftrightarrow\) (t + x)(t + 2x) = 0

Thay t = x2 + 4x + 8 ta được:

(x2 + 4x + 8 + x)(x2 + 4x + 8 + 2x) = 0

\(\Leftrightarrow\) (x2 + 5x + 8)[x(x + 4) + 2(x + 4)] = 0

\(\Leftrightarrow\) (x2 + 5x + \(\frac{25}{4}\) + \(\frac{7}{4}\))(x + 4)(x + 2) = 0

\(\Leftrightarrow\) [(x + \(\frac{5}{2}\))2 + \(\frac{7}{4}\)](x + 4)(x + 2) = 0

Vì (x + \(\frac{5}{2}\))2 + \(\frac{7}{4}\) > 0 với mọi x

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

Vậy S = {-4; -2}

Mình giúp bn phần khó thôi!

Chúc bn học tốt!!

22 tháng 4 2020

c) \(\frac{1}{x-1}\)+\(\frac{2x^2-5}{x^3-1}\)=\(\frac{4}{x^2+x+1}\) (ĐKXĐ:x≠1)

\(\frac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\)+\(\frac{2x^2-5}{\left(x-1\right)\left(x^2+x+1\right)}\)=\(\frac{4\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)

⇒x2+x+1+2x2-5=4x-4

⇔3x2-3x=0

⇔3x(x-1)=0

⇔x=0 (TMĐK) hoặc x=1 (loại)

Vậy tập nghiệm của phương trình đã cho là:S={0}

11 tháng 5 2020

\(x^3-6x^2+5x+12>0\\ < =>\left(x^3-5x-x+5x\right)+12>0\\ < =>\left[\left(x^3-x\right)-\left(5x-5x\right)\right]+12>0\\ < =>x^2+12>0\\ < =>x^2>-12\\ =>x\in R\\ BPTcóvôsốnghiem\)

31 tháng 12 2019

a) (2x - 1)(3x + 5) - 2(-4x + 1)2 = 6x2 + 10x - 3x - 5 - 2(16x2 - 8x + 1) = 6x2 - 3x - 5 - 32x2 + 16x - 2 = -26x2 + 13x - 7

b) \(\frac{x^2-16}{4x-x^2}=\frac{\left(x-4\right)\left(x+4\right)}{-x\left(x-4\right)}=-\frac{x+4}{x}\)

c) \(\frac{2x-9}{x^2-5x+6}+\frac{2x+1}{x-3}+\frac{x+3}{2-x}\)

\(\frac{2x-9}{x^2-2x-3x+6}+\frac{\left(2x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}-\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}\)

\(\frac{2x-9+2x^2-3x-2-x^2+9}{\left(x-3\right)\left(x-2\right)}\)

\(\frac{x^2-x-2}{\left(x-3\right)\left(x-2\right)}\)

\(\frac{x^2-2x+x-2}{\left(x-3\right)\left(x-2\right)}\)

\(\frac{\left(x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}=\frac{x+1}{x-3}\)

d) (x - 1)3 - (x + 1)3 + 6(x + 1)(x - 1)

= (x - 1 - x - 1)[(x - 1)2 + (x - 1)(x + 1) + (x + 1)2] + 6(x2 - 1)

= -2(x2 - 2x + 1  + x2 - 1 + x2 + 2x + 1) + 6x2 - 6

= -2(3x2 + 1) + 6x2 - 6

= -6x2 - 2 + 6x2  - 6

= -8

e) (2x + 7)2 - (4x + 14)(2x - 8) + (8 - 2x)2

= (2x + 7)2 - 2(2x + 7)(2x - 8) + (2x - 8)2

= (2x + 7 - 2x + 8)2

= 152 = 225

21 tháng 12 2019
https://i.imgur.com/u2NWDkL.jpg
21 tháng 12 2019
https://i.imgur.com/Ls5Q93L.jpg
24 tháng 6 2017

a) Ta có : x2 - 4x + 3

= x2 - x - 3x + 3

= x(x - 1) - (3x - 3) 

= x(x - 1) - 3(x - 1)

= (x - 1) (x - 3) 

24 tháng 6 2017

a) \(x^2-4x+3\)

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

\(=x\left(x-1\right)-3\left(x-1\right)\)

\(=\left(x-1\right)\left(x-3\right)\)

b) \(x^2+5x+4\)

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

\(=x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x+4\right)\)

c) \(x^2-x-6\)

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

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

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

d) \(x^4+1997x^2+1996x+1997\)

\(=x^4+x^2+1996x^2+1996x+1996+1\)

\(=\left(x^4+x^2+1\right)+\left(1996x^2+1996x+1996\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+1996\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)

e) \(x^2-2001\cdot2002\)( hình như sai sai)

21 tháng 8 2020

a/\(\left(4x-1\right)\left(x+5\right)=x^2-25\Leftrightarrow4x^2+20x-x-5=x^2-25\Leftrightarrow3x^2+19x+20\)\(\Leftrightarrow\left[{}\begin{matrix}\frac{-4}{3}\\-5\end{matrix}\right.\)

b/

\(2x^3-6x^2=x^2-3x\Leftrightarrow2x^3-6x^2-x^2+3x=0\Leftrightarrow2x^2\left(x-3\right)-x\left(x-3\right)=0\Leftrightarrow\left(2x^2-x\right)\left(x-3\right)=0\)\(\Leftrightarrow\left[{}\begin{matrix}2x^2-x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\frac{1}{2}\\3\\0\end{matrix}\right.\)

c/\(x\left(x+3\right)^3-\frac{x}{4}\left(x+3\right)=0\Leftrightarrow\left(x+3\right)\left[\left(x+3\right)^2x-\frac{x}{4}\right]=0\Leftrightarrow\left(x+3\right)\left[\left(x^2+6x+9\right)x-\frac{x}{4}\right]=0\Leftrightarrow\left(x+3\right)\left(x^3+6x^2+9x-\frac{x}{4}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x^3+6x^2+\frac{35}{4}x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\frac{5}{2}\\x=-\frac{7}{2}\end{matrix}\right.\)

d/\(\left(x-1\right)^2=\left(2x+5\right)^2\Leftrightarrow\left(x-1\right)^2-\left(2x+5\right)^2=0\Leftrightarrow\left(x-1+2x+5\right)\left(x-1-2x-5\right)=0\Leftrightarrow\left(3x+4\right)\left(-x-6\right)=0\Leftrightarrow\left[{}\begin{matrix}3x+4=0\\x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\frac{-4}{3}\\0\\-6\end{matrix}\right.\)