(x -2)+3x2-6x=0 Giúp mk vs
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a) Ta có : \(x^2-6x+10\)
\(=\left(x^2-6x+9\right)+1\)
\(=\left(x-3\right)^2+1\ge1>0\forall x\)
b) Ta có : \(4x-x^2-5\)
\(=-\left(x^2-4x+4\right)-1\)
\(=-\left(x-2\right)^2-1\le-1< 0\forall x\)
Vậy ...
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a: Ta có: \(x^2-8x+20\)
\(=x^2-8x+16+4\)
\(=\left(x-4\right)^2+4>0\forall x\)
b: Ta có: \(-x^2+6x-19\)
\(=-\left(x^2-6x+19\right)\)
\(=-\left(x^2-6x+9+10\right)\)
\(=-\left(x-3\right)^2-10< 0\forall x\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x-1\right)3+3x\left(x-1\right)=0\)
<=> \(3\left(x-1\right)\left(x+1\right)=0\)
<=> \(\orbr{\begin{cases}x-1=0\\x+1=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
Vậy...
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\(a,=\left(x-2\right)^2\\ b,=\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\\ c,=\left(1-2x\right)\left(1+2x+4x^2\right)\\ d,=\left(x+1\right)^3\\ e,Sửa:\left(x+y\right)^2-9x^2=\left(x+y-3x\right)\left(x+y+3x\right)\\ =\left(y-2x\right)\left(4x+y\right)\\ f,=\left(x+3\right)^2\\ g,=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\\ h,=8\left(x^3-\dfrac{1}{64}\right)=8\left(x-\dfrac{1}{4}\right)\left(x^2+\dfrac{1}{4}x+\dfrac{1}{16}\right)\)
a) \(\left(x-2\right)^2\)
b) \(\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
c) \(\left(1-2x\right)\left(1+2x+4x^2\right)\)
d) \(\left(x+1\right)^3\)
e) \(\left(x+y-3\sqrt{x}\right)\left(x+y+3\sqrt{x}\right)\)
f) \(\left(x+3\right)^2\)
g) \(-\left(x-5\right)^2\)
h) \(\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow\left(x+2\right)\left(5-3x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{5}{3}\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`x^4+6x^2-6x+14=0`
`<=>x^4+5x^2+6+x^2-6x+9=0`
`<=>x^4+5x^2+6+(x-3)^2=0`vô lý
Vì `x^4+5x^2+6+(x-3)^2>=6>0`
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\Leftrightarrow3x\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\\ b,\Leftrightarrow x\left(x-1\right)+2\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-6x+11=\left(x^2-6x+9\right)+2\)\(=\left(x-3\right)^2+2\)
Vì \(\left(x-3\right)^2\ge0\Leftrightarrow\left(x-3\right)^2+2\ge2\)
Mặt khác 2 > 0 nên \(\left(x-3\right)^2+2>0\Leftrightarrow x^2-6x+11>0\)\(\forall x\inℝ\)
<=>(x-2)+3x(x-2)=0
<=>(x-2)(1+3x)=0
<=>\(\orbr{\begin{cases}x-2=0\\1+3x=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=2\\x=-\frac{1}{3}\end{cases}}\)
Vậy x=2 hoặc x=-1/3