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1: =>3x(x-20)-(x-20)=0
=>(x-20)(3x-1)=0
=>x=1/3 hoặc x=20
3: \(\Leftrightarrow x^2\left(x^3+1\right)=0\)
=>x=0 hoặc x=-1
4: \(\Leftrightarrow x\left(x-3\right)-3\left(x-3\right)=0\)
=>(x-3)2=0
=>x=3
1: \(\Leftrightarrow3x+4x=4\)
=>7x=4
hay x=4/7
2: \(\Leftrightarrow3x-5x-5^3:5^2=0\)
=>-2x=5
=>x=-5/2
b, x = -5/3 hoặc x = 4/3.
c, x = 0 hoặc x = 3, -3.
d, x = 0 hoặc x = 2, -2.
e, x = 1 hoặc x = \(\dfrac{-1}{2}\).
a: \(\Leftrightarrow x^2-40x+400-x^2-4x-3=-7\)
=>-44x+397=-7
=>-44x=-404
hay x=101
b: \(\Leftrightarrow\left[{}\begin{matrix}3x+5=0\\4-3x=0\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{5}{3};\dfrac{4}{3}\right\}\)
c: \(\Leftrightarrow x\left(x^2-9\right)=0\)
=>x(x-3)(x+3)=0
hay \(x\in\left\{0;3;-3\right\}\)
d: \(\Leftrightarrow x\left(x-2\right)\left(x+2\right)=0\)
hay \(x\in\left\{0;2;-2\right\}\)
e: =>(2x+1)(1-x)=0
=>x=-1/2 hoặc x=1
2. \(-x^2+2x-2=-\left(x^2+2x+1\right)-1=-\left(x+1\right)^2-1\)
vì: \(-\left(x+1\right)^2\forall x\le0\Rightarrow-\left(x+1\right)^2-1\le-1< 0\left(đpcm\right)\)
6.
\(\left(x-2\right)\left(x-4\right)+3=x^2-6x+11=\left(x^2-6x+9\right)+2=\left(x-3\right)^2+2\)
vì: \(\left(x-3\right)^2\ge0\forall x\Rightarrow\left(x-3\right)^2+2\ge2>0\left(đpcm\right)\)
1.(x+1)(x-7)+17=(x-3)2+1>0
2.-20-(x-5)(x+3)=-34-(x-1)2<0
3.-2(x+3)-(x-2)(x+2)=-(x+1)2-1<0
4.x2+y2+2x+2y+3=(x+1)2+(y+1)2+1>0
5.2x2+2x+y2+2y+5=2(x+1/2)2+(y+1)2+2>0
6.2x2+2y2+2xy+2x+4y+6=(x+y)2+(x+1)2+(y+2)2+1>0
7.-y2+4y-4-/x+1/=-(y-2)2-/x+1/≤0
Giải:
1) \(9x^2-12xy+4y^2-3\)
\(=\left(3x-2y\right)^2-3\)
\(=\left(3x-2y-\sqrt{3}\right)\left(3x-2y+\sqrt{3}\right)\) (Bước này chắc không cần)
2) \(x^2+4x+1\)
\(=x^2+4x+4-3\)
\(=\left(x+2\right)^2-3\)
\(=\left(x+2-\sqrt{3}\right)\left(x+2+\sqrt{3}\right)\)
(Bước này chắc không cần)
3) \(x^2-4x+7\)
\(=x^2-4x+4+3\)
\(=\left(x-2\right)^2+3\)
4) \(x^2+6x+15\)
\(=x^2+6x+9+6\)
\(=\left(x+3\right)^2+6\)
5) \(x^2-x+\dfrac{1}{3}\)
\(=x^2-x+\dfrac{1}{4}+\dfrac{1}{12}\)
\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{12}\)
6) \(\dfrac{1}{4}x^2+x\)
\(=\left(\dfrac{1}{2}x\right)^2+x+1-1\)
\(=\left(\dfrac{1}{2}x+1\right)^2-1\)
7) \(3x^2+2x+1\)
\(=x^2+2x+1+2x^2\)
\(=\left(x+1\right)^2+2x^2\)
8) \(2x^2-2x+1\)
\(=x^2-2x+1+x^2\)
\(=\left(x-1\right)^2+x^2\)
9) \(10a^2+5b^2+12ab+4a-6b+15\)
\(=4a^2+6a^2+4b^2+b^2+12ab+4a-6b+15\)
\(=\left(6a^2+b^2+12ab\right)+4a+4a^2-6b+4b^2+15\)
\(=\left(6a+b\right)^2+4a\left(1+a\right)-2b\left(3+2b\right)+15\)
Giải:
1) \(9x^2-12xy+4y^2-3\)
\(=\left(9x^2-12xy+4y^2\right)-3\)
\(=\left(3x-2y\right)^2-3\)
2) \(x^2+4x+1\)
\(=x^2+4x+4-3\)
\(=\left(x+2\right)^2-3\)
3) \(x^2-4x+7\)
\(=x^2-4x+4+3\)
\(=\left(x-2\right)^2+3\)
4) \(x^2+6x+15\)
\(=x^2+6x+9+6\)
\(=\left(x+3\right)^2+6\)
5) \(x^2-x+\dfrac{1}{3}\)
\(=x^2-x+\dfrac{1}{4}+\dfrac{1}{12}\)
\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{12}\)
6) \(\dfrac{1}{4}x^2+x\)
\(=x\left(\dfrac{1}{4}x+1\right)\)
7) \(3x^2+2x+1\)
\(=x^2+2x+1+2x^2\)
\(=\left(x+1\right)^2+2x^2\)
8) \(2x^2-2x+1\)
\(=x^2-2x+1+x^2\)
\(=\left(x-1\right)^2+x^2\)
9) \(10a^2+5b^2+12ab+4a-6b+15\)
\(=a^2+b^2+9a^2+12ab+4b^2+4a-6b+15\)
\(=9a^2+12ab+4b^2+a^2+4a-6b+b^2+15\)
\(=\left(3a+2b\right)^2+a\left(a+4\right)-b\left(6-b\right)+15\)
Vậy ...
1) \(-6x^2-x+7=0\)
\(\Leftrightarrow-6x^2+6x-7x+7=0\)
\(\Leftrightarrow\left(-6x^2+6x\right)-\left(7x-7\right)=0\)
\(\Leftrightarrow-6x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(-6x-7\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-6x-7=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{6}\\x=1\end{matrix}\right.\)
2) \(-4x^2-5x+9=0\)
\(\Leftrightarrow-4x^2+4x-9x+9=0\)
\(\Leftrightarrow\left(-4x^2+4x\right)-\left(9x-9\right)=0\)
\(\Leftrightarrow-4x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(-4x-9\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x-9=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{9}{4}\\x=1\end{matrix}\right.\)
3) \(x^2+3x-4=0\)
\(\Leftrightarrow x^2-x+4x-4=0\)
\(\Leftrightarrow\left(x^2-x\right)+\left(4x-4\right)=0\)
\(\Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
4) \(x^2-6x-7=0\)
\(\Leftrightarrow x^2+x-7x-7=0\)
\(\Leftrightarrow\left(x^2+x\right)-\left(7x+7\right)=0\)
\(\Leftrightarrow x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\)
5) \(x^2+5x+4=0\)
\(\Leftrightarrow x^2+x+4x+4=0\)
\(\Leftrightarrow\left(x^2+x\right)+\left(4x+4\right)=0\)
\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
a) \(-6x^2-x+7=0\)
\(\Leftrightarrow-6x^2+6x-7x+7=0\)
\(\Leftrightarrow-6x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-6x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-7}{6}\end{matrix}\right.\)
b) \(-4x^2-5x+9=0\)
\(\Leftrightarrow-4x^2+4x-9x+9=0\)
\(\Leftrightarrow-4x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-4x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2,25\end{matrix}\right.\)
c) \(x^2+3x-4=0\)
\(\Leftrightarrow x^2-x+4x-4=0\)
\(\Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-4\end{matrix}\right.\)
d) \(x^2-6x-7=0\)
\(\Leftrightarrow x^2+x-7x-7=0\)
\(\Leftrightarrow x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=7\end{matrix}\right.\)
e) \(x^2+5x+4=0\)
\(\Leftrightarrow x^2+x+4x+4=0\)
\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4\end{matrix}\right.\)
1,\(x^4-x=0\\ ->x\left(x-1\right)\left(x^2+x+1\right)=0\\ ->\left(......\right)\)
2\(x^4-x^2=0\\ ->x^2\left(x^2-1\right)\\ ->x^2\left(x-1\right)\left(x+1\right)\\ ->......\)
3,\(x^5+x^2\\ ->x^2\left(x^3+1\right)\\ ->x^2\left(x+1\right)\left(x^2-x+1\right)\\ ->.......\)
4\(3x\left(x-20\right)-x+20=0->\left(3x-1\right)\left(x-20\right)=0->.....\)