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Bài 2:
a: \(\Leftrightarrow2x^2-10x-3x-2x^2=26\)
=>-13x=26
hay x=-2
b: \(\Leftrightarrow\left(x-1\right)\left(5x-1\right)=0\)
hay \(x\in\left\{1;\dfrac{1}{5}\right\}\)
c: \(\Leftrightarrow\left(x+5\right)\left(2-x\right)=0\)
hay \(x\in\left\{-5;2\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có
x 3 – 12 x 2 + 48 x – 64 = 0 ⇔ x 3 – 3 . x 2 . 4 + 3 . x . 4 2 – 4 3 = 0 ⇔ ( x – 4 ) 3 = 0
ó x – 4 = 0 ó x = 4
Vậy x = 4
Đáp án cần chọn là: B
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Delta=b^2-4ac=\left(-48\right)^2-4.1.\left(-25\right)=2400>0\)
do đó pt có 2 nghiệm phân biệt là:
\(•x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{48-\sqrt{2400}}{2}=24-10\sqrt{6}\\ •x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{48+\sqrt{2400}}{2}=24+10\sqrt{6}\)
\(x^2-48x-25=0\)
\(\Leftrightarrow x^2-2.x.24+24^2-601=0\)
\(\Leftrightarrow\left(x-24\right)^2-601=0\)
\(\Leftrightarrow\left(x-24\right)^2=601\)
\(\Leftrightarrow x-24=\sqrt{601}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-24=\sqrt{601}\\x-24=-\sqrt{601}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=24+\sqrt{601}\\x=24-\sqrt{601}\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3x^3-75x=0\Leftrightarrow3x\left(x^2-25\right)=0\Leftrightarrow3x\left(x-5\right)\left(x+5\right)=0\Leftrightarrow x=0;x=-5;x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3+3x^2+2x=0\)
\(\Leftrightarrow x\left(x^2+3x+2\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=-2\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^4+3x^3-x-3=0\)
\(\Leftrightarrow x^3\left(x+3\right)-\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^3-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x^3-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)
Vậy \(x\in\left\{-3;1\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b: \(8x^2-48x+6xy-36y\)
\(=8x\left(x-6\right)+6y\left(x-6\right)\)
\(=2\left(x-6\right)\left(4x+3y\right)\)
d: \(a^2-2ab+b^2-4\)
\(=\left(a-b\right)^2-4\)
\(=\left(a-b-2\right)\left(a-b+2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{1) }3x^3-48x=0\\ \Leftrightarrow x\left(3x^2-48\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x^2-48=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\3x^2=48\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm4\end{matrix}\right.\\ \text{Vậy }x=0\text{ hoặc }x=\pm4\)
\(\text{2) }x^3+x^2-4x=4\\ \Leftrightarrow x^3+x^2-4x-4=0\\ \Leftrightarrow\left(x^3+x^2\right)-\left(4x+4\right)=0\\ \Leftrightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\\ \Leftrightarrow\left(x^2-4\right)\left(x+1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=1\end{matrix}\right.\\ \text{Vậy }x=2\text{ hoặc }x=-2\text{ hoặc }x=1\)
1) \(3x^3-48x=0\)
\(\Leftrightarrow3x\left(x^2-16\right)=0\)
\(\Leftrightarrow3x\left(x^2-4^2\right)=0\)
\(\Leftrightarrow3x\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=0\\x-4=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
Vậy x=0 ; x=4 ; x=-4
b) \(x^3+x^2-4x=4\)
\(\Leftrightarrow x^3+x^2-4x-4=0\)
\(\Leftrightarrow\left(x^3+x^2\right)-\left(4x+4\right)=0\)
\(\Leftrightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-2^2\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\\x=-2\end{matrix}\right.\)
Vậy x=-1 ; x=2 ; x=-2
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : x4+3x3+4x2+3x+1=0
⇔ ( x4 + x3 ) + ( 2x3 + 2x2 ) + ( 2x2 + 2x ) + ( x + 1 ) = 0
⇔ x3 ( x + 1 ) + 2x2 ( x + 1 ) + 2x ( x+1 ) + ( x + 1 ) =0
⇔ ( x + 1 ) ( x3 + 2x2 + 2x + 1 ) = 0
⇔ ( x + 1 ) [ ( x3 + 1 ) + ( 2x2 + 2x ) ] = 0
⇔ ( x + 1 ) [ (x + 1 ) ( x2 - x +1 ) + 2x ( x + 1 ) ] =0
⇔ ( x +1 ) ( x + 1 ) ( x2 + x +1 ) =0
⇒ \(\left[{}\begin{matrix}x+1=0\\x^{2^{ }}+x+1=0\end{matrix}\right.\)<=> \(\left[{}\begin{matrix}x=-1\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}=0\left(VoLy\right)\end{matrix}\right.\)
Vậy x = -1
x4+3x3+4x2+3x+1=0
⇔(x4+2x3+x2)+(x3+2x2+1)+(x2+2x+1)=0
⇔x2(x2+2x+1)+x(x2+2x+1)+(x2+2x+1)=0
⇔x2(x+1)2+x(x+1)2+(x+1)2=0
⇔(x+1)2(x2+x+1)=0
Vì x2+x+1=x2+x+\(\dfrac{1}{4}\)+\(\dfrac{3}{4}\)=(x+\(\dfrac{1}{2}\))2+\(\dfrac{3}{4}\)>0 nên phương trình đã cho tương đương:
(x+1)2=0 ⇔(x+1)(x+1)=0 ⇔x=-1.
3x3 - 48x = 0
=> 3x( x2 - 16) = 0
=> x = 0 hoặc x2 -16 = 0
x2 - 16 = 0 => x2 = 16 => x = 4 hoặc x =-4