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b)x^3 - 6x^2 +11x-6=0
<=>x^3 - x^2 - 5x^2 +5x + 6x - 6=0
<=>x^2(x - 1) - 5x(x - 1) +6(x - 1)=0
<=>(x-1).(x^2 - 5x + 6)=0
<=>(x - 1).(x^2 - 2x - 3x + 6)=0
<=>(x - 1).[(x(x-2)-3(x-2)]=0
<=>(x-1)(x-2)(x-3)=0
<=>x-1=0hoac x-2=0 hoac x-3=0
<=>x=1hoac x=2 hoac x=3
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\(x^3-2x^2+x=0\)
\(\Leftrightarrow x\left(x^2-2x+1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)^2=0\)
\(\Rightarrow x=0;x=1\)
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1)
a) \(x^3-5x^2+x-5=0\Rightarrow x^2.\left(x-5\right)+\left(x-5\right)\)
\(\Rightarrow\left(x^2+1\right).\left(x-5\right)=0\Rightarrow\orbr{\begin{cases}x^2+1=0\\x-5=0\end{cases}\Rightarrow}\orbr{\begin{cases}x^2=-1\left(sai\right)\\x=5\end{cases}}\)\(KL:x=5\)
b) \(x^4-2x^3+10x^2-20x=0\Rightarrow x^3.\left(x-2\right)+10x\left(x-2\right)\)
\(\Rightarrow\left(x-2\right).\left(x^3+10x\right)\Rightarrow\orbr{\begin{cases}x-2=0\\x^3+10x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x\left(x^2+10\right)=0\Rightarrow x=0\end{cases}}\)
Vì nếu x2 + 10 = 0 => x2 = -10 ( sai )
Vậy...
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\(1.6x\left(x-10\right)-2x+20=0\)
⇔\(6x\left(x-10\right)-2\left(x-10\right)=0\)
⇔ \(2\left(x-10\right)\left(3x-1\right)=0\)
⇔ x = 10 hoặc x = \(\dfrac{1}{3}\)
KL....
\(2.3x^2\left(x-3\right)+3\left(3-x\right)=0\)
⇔ \(3\left(x-3\right)\left(x^2-1\right)=0\)
⇔ \(x=+-1\) hoặc \(x=3\)
KL....
\(3.x^2-8x+16=2\left(x-4\right)\)
⇔ \(\left(x-4\right)^2-2\left(x-4\right)=0\)
⇔ \(\left(x-4\right)\left(x-6\right)=0\)
⇔ \(x=4\) hoặc \(x=6\)
KL.....
\(4.x^2-16+7x\left(x+4\right)=0\)
\(\text{⇔}4\left(x+4\right)\left(2x-1\right)=0\)
⇔ \(x=-4hoacx=\dfrac{1}{2}\)
KL.....
\(5.x^2-13x-14=0\)
⇔ \(x^2+x-14x-14=0\)
\(\text{⇔}\left(x+1\right)\left(x-14\right)=0\)
\(\text{⇔}x=14hoacx=-1\)
KL......
Còn lại tương tự ( dài quá ~ )
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(x^4-10x^3+25x^2=0\)
\(\Leftrightarrow x^2\left(x^2-10x+25\right)=0\)
\(\Leftrightarrow x^2\left(x-5\right)^2=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x^2=0\\\left(x-5\right)^2=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=5\end{array}\right.\)
b) \(x^3+3x^2+3x+1=0\)
\(\Leftrightarrow\left(x+1\right)^3=0\)
\(\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x4 - 10x3 + 25x2 = (x2)2 - 2.x2.5x + (5x)2 = (x2 - 5x)2 = 0 => x(x - 5) = 0 => x = 0 hay x - 5 = 0 => x = 0 ; 5
b) x3 + 3x2 + 3x + 1 = x3 + 3.x2.1 + 3.x.12 + 13 = (x + 1)3 = 0 => x + 1 = 0 => x = -1
a,x^2(x^2-10x+25)=0
x^2(x-5)^2=0
=> x^2=0 hoac (x-5)^2=0
=>x=0 hoac 5
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left(x^2-1\right)\left(x^2-25\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-1=0\\x^2-25=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2=1\\x^2=25\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm1\\x=\pm5\end{cases}}\)
b) \(x^2-8x+16=0\)
\(\Leftrightarrow\left(x-4\right)^2=0\)
\(\Leftrightarrow x-4=0\)
\(\Leftrightarrow x=4\)
c) \(x^3+3x^2+3x+1=0\)
\(\Leftrightarrow\left(x+1\right)^3=0\)
\(\Leftrightarrow x+1=0\)
\(\Rightarrow x=-1\)
d) \(x^3+10x^2+25x=0\)
\(\Leftrightarrow x\left(x+5\right)^2=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)
a) ( x2 - 1 )( x2 - 25 ) = 0
<=> \(\orbr{\begin{cases}x^2-1=0\\x^2-25=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm1\\x=\pm5\end{cases}}\)
b) x2 - 8x + 16 = 0
<=> ( x - 4 )2 = 0
<=> x - 4 = 0
<=> x = 4
c) x3 + 3x2 + 3x + 1 = 0
<=> ( x + 1 )3 = 0
<=> x + 1 = 0
<=> x = -1
d) x3 + 10x2 + 25x = 0
<=> x( x2 + 10x + 25 ) = 0
<=> x( x + 5 )2 = 0
<=> \(\orbr{\begin{cases}x=0\\x+5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)