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23 tháng 1 2017

=(x2+7x+12)-a2+a=0

=(x+3)(x+4)-a2+a=0

Đặt x+3=y.Ta có

=y2+y-a2+a=0

=(y-a+1)(y+a)=0

=>y=a-1,y=-a

mà x+3=y

=>x=a-4 và x=-a-3

27 tháng 12 2017

\(x^2+7x-a^2+a+12=0\)

\(\Leftrightarrow x^2-ax+4x+ax+3x-a^2+a+12=0\)

\(\Leftrightarrow\left(x^2-ax+4x\right)+\left(ax+3x\right)-\left(a^2+3a\right)+\left(4a+12\right)=0\)

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

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

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

\(\Leftrightarrow\orbr{\begin{cases}x+a+3=0\\x-a+4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-a-3\\x=a-4\end{cases}}}\)

Vậy \(x=-a-3\) hoặc \(x=a-4\)

11 tháng 9 2018

a. A= x2-7x+20 = x2-2*\(\dfrac{7}{2}x+\dfrac{49}{4}+\dfrac{31}{4}\)=(x-\(\dfrac{7}{2}\))2+\(\dfrac{31}{4}\)>0 \(\forall x\)(đpcm)

b. B= 2x2+5x+14=2(x2+2*\(\dfrac{5}{4}x+\dfrac{25}{16}+\dfrac{87}{16}\))=2(x+\(\dfrac{5}{4}\))2+\(\dfrac{87}{8}\)>0(đpcm)

11 tháng 9 2018

thanks you !!!hehe


a) Ta có: \(x^2-3x+2=0\)

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

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

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

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

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

Vậy: \(x\in\left\{1;2\right\}\)

b) Ta có: \(-x^2+5x-6=0\)

\(\Leftrightarrow-\left(x^2-5x+6\right)=0\)

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

\(\Leftrightarrow-\left[\left(x^2-2x\right)-\left(3x-6\right)\right]=0\)

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

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

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

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

Vậy: x∈{2;3}

c) Ta có: \(4x^2-12x+5=0\)

\(\Leftrightarrow4x^2-10x-2x+5=0\)

⇔(4x2-10x)-(2x-5)=0

\(\Leftrightarrow2x\left(2x-5\right)-\left(2x-5\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}2x-5=0\\2x-1=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}2x=5\\2x=1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{5}{2}\\x=\frac{1}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{\frac{1}{2};\frac{5}{2}\right\}\)

d) Ta có: \(2x^2+5x+3=0\)

\(\Leftrightarrow2x^2+2x+3x+3=0\)

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

\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)=0\)

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

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

Vậy: \(x\in\left\{-1;\frac{-3}{2}\right\}\)

e) Ta có: \(x^3+2x^2-x-2=0\)

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

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

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

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

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

Vậy: \(x\in\left\{-2;1;-1\right\}\)

g) Ta có: \(\left(3x-1\right)^2-5\left(2x+1\right)^2+\left(6x-3\right)\left(2x+1\right)=\left(x-1\right)^2\)

\(\Leftrightarrow9x^2-6x+1-20x^2-20x-5+12x^2-3-x^2+2x-1=0\)

\(\Leftrightarrow-24x-8=0\)

\(\Leftrightarrow-8\left(3x+1\right)=0\)

⇔3x+1=0

\(\Leftrightarrow3x=-1\)

\(\Leftrightarrow x=-\frac{1}{3}\)

Vậy: \(x=-\frac{1}{3}\)

22 tháng 1 2020

h) \(2x^3-7x^2+7x-2=0\)

\(\Leftrightarrow2x^3-4x^2-3x^2+6x+x-2=0\)

\(\Leftrightarrow2x^2\left(x-2\right)-3x\left(x-2\right)+\left(x-2\right)=0\)

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

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

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

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

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

Vậy S = {2; 1; \(\frac{1}{2}\)}

i) \(x^4+2x^3+5x^2+4x-12=0\)

\(\Leftrightarrow x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12=0\)

\(\Leftrightarrow x^3\left(x-1\right)+3x^2\left(x-1\right)+8x\left(x-1\right)+12\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3+3x^2+8x+12\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3+2x^2+x^2+2x+6x+12\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x+2\right)+x\left(x+2\right)+6\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left[\left(x+\frac{1}{2}\right)^2+\frac{23}{4}\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\\\left(x+\frac{1}{2}\right)^2+\frac{23}{4}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\\\left(x+\frac{1}{2}\right)^2=\frac{-23}{4}\left(loai\right)\end{matrix}\right.\)

Vậy S = {1;-2}

15 tháng 12 2019

a) \(x^2-2x=0\)

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

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

b) \(x^2-7x+12=0\)

\(x^2-4x-3x+12=0\)

\(\left(x^2-3x\right)-\left(4x-12\right)=0\)

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

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

\(\Rightarrow\orbr{\begin{cases}x-4=0\\x-3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=4\\x=3\end{cases}}}\)

a) \(x^2-2x=0\)

  \(x\left(x-2\right)=0\)

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

b) \(x^2-7x+12=0\)

   \(x^2-3x-4x+12=0\)

    \(\left(x^2-3x\right)-\left(4x-12\right)=0\)

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

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

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-4=0\end{cases}}\)                    \(\Rightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}\)

Ukm

It's very hard

l can't do it 

Sorry!

 
27 tháng 7 2018

a) \(x^4-x^3-7x^2+x+6=0\)

\(\Leftrightarrow x^4+2x^3-3x^3-6x^2-x^2-2x+3x+6=0\)

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

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

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

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

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x-3\right)=0\). Làm nốt

b) \(2x^2+2xy+y^2+9=6x-\left|y+3\right|\)

\(\Leftrightarrow2x^2+2xy+y^2+9-6x+\left|y+3\right|=0\)

\(\Leftrightarrow\left(x^2+2xy+y^2\right)+x^2-6x+9+\left|y+3\right|=0\)

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

Do \(\left(x+y\right)^2\ge0;\left(x-3\right)^2\ge0;\left|y+3\right|\ge0\forall x;y\)

\(\Rightarrow\hept{\begin{cases}x+y=0\\x-3=0\\y+3=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=3\\y=-3\end{cases}}\)

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

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

\(\Leftrightarrow\left(2x^2+x-2\right)^2=1\Leftrightarrow\orbr{\begin{cases}2x^2+x-2=1\\2x^2+x-2=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x^2+x-3=0\\2x^2+x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2+2.x.\frac{1}{4}+\frac{1}{16}-\frac{1}{16}-\frac{3}{2}=0\\x^2+2.x.\frac{1}{4}+\frac{1}{16}-\frac{1}{16}-\frac{1}{2}=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}\left(x+\frac{1}{4}\right)^2-\frac{25}{16}=0\\\left(x+\frac{1}{4}\right)^2-\frac{9}{16}=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}\left(x+\frac{1}{4}\right)^2=\frac{25}{16}\\\left(x+\frac{1}{4}\right)^2=\frac{9}{16}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{4}=\pm\frac{5}{4}\\x+\frac{1}{4}=\pm\frac{3}{4}\end{cases}}\)

Từ đó tính đc x

d) \(\left(x^2+3x+2\right)\left(x^2+7x+12\right)=24\)

\(\Leftrightarrow\left(x^2+x+2x+2\right)\left(x^2+3x+4x+12\right)=24\)

\(\Leftrightarrow\left[x\left(x+1\right)+2\left(x+1\right)\right]\left[x\left(x+3\right)+4\left(x+3\right)\right]=24\)

\(\Leftrightarrow\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24=0\)

\(\Leftrightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24=0\)

Đặt \(x^2+5x+5=a\), khi đó pt có dạng:

\(\left(a-1\right)\left(a+1\right)-24=0\Leftrightarrow a^2-1-24=0\)

\(\Leftrightarrow a^2-25=0\Leftrightarrow\left(a-5\right)\left(a+5\right)=0\Leftrightarrow\orbr{\begin{cases}a=5\\a=-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x^2+5x+5=5\\x^2+5x+5=-5\end{cases}}\Leftrightarrow\orbr{\begin{cases}x\left(x+5\right)=0\\x^2+5x+10=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x\left(x+5\right)=0\\x^2+2.x.\frac{5}{2}+\frac{25}{4}+\frac{15}{4}=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x\left(x+5\right)=0\\\left(x+\frac{5}{4}\right)^2=-\frac{15}{4}\left(vn\right)\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)

14 tháng 3 2017

Bài 2

Ta có :

\(x^2+5x+6=\left(x+2\right)\left(x+3\right)\)

\(x^2+7x+12=\left(x+3\right)\left(x+4\right)\)

\(x^2+9x+20=\left(x+4\right)\left(x+5\right)\)

Khi đó:

\(\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}=\dfrac{3}{40}\)

=> \(\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}=\dfrac{3}{40}\)

=> \(\dfrac{1}{x+2}-\dfrac{1}{x+3}+\dfrac{1}{x+3}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+5}=\dfrac{3}{40}\)

=> \(\dfrac{1}{x+2}-\dfrac{1}{x+5}=\dfrac{3}{40}\)

Giải phương trình ta được x = 3