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17 tháng 6 2016
b)
\(\left(2x-1\right)^2=25\)
\(\left(2x-1\right)^2=5^2=\left(-5\right)^2\)
TH1: 2x - 1 = 5
=> x = 3
TH2: 2x - 1 = -5
=> x = -2
17 tháng 6 2016
a) \(x^3-0,25x=0\Leftrightarrow4x^3-x=0\Leftrightarrow x\left(4x^2-1\right)=0\Leftrightarrow x\left(2x-1\right)\left(2x+1\right)=0\)
\(\Leftrightarrow x=0\)hoặc \(x=\frac{1}{2}\)hoặc \(x=-\frac{1}{2}\)
b) \(\left(2x-1\right)^2-25=0\Leftrightarrow\left(2x-1\right)^2-5^2=0\Leftrightarrow\left(2x-6\right)\left(2x+4\right)=0\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}\)
c) \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\Leftrightarrow\left(x+2\right)\left[\left(x+2\right)-\left(x-2\right)\right]=0\Leftrightarrow\left(x+2\right).4=0\Leftrightarrow x=-2\)
PT
2
TN
13 tháng 6 2017
\(x^3-0,25x=0\)
\(\Leftrightarrow x\left(x^2-0,25\right)=0\)
\(\Leftrightarrow x\left(x-0,5\right)\left(x+0,5\right)=0\)
<=>x=0 hoặc x-0,5=0 hoặc x+0,5=0
<=>x=0 hoặc x=0,5 hoặc x=-0,5
13 tháng 11 2021
\(\Leftrightarrow x\left(2x-3\right)-2\left(2x-3\right)=0\\ \Leftrightarrow\left(x-2\right)\left(2x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{3}{2}\end{matrix}\right.\)
13 tháng 11 2021
\(x\left(2x-3\right)-2\left(2x-3\right)=0\Rightarrow\left(2x-3\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=2\end{matrix}\right.\)
NT
2
H9
HT.Phong (9A5)
CTVHS
1 tháng 9 2023
c) \(x^2-9=2\cdot\left(x+3\right)^2\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)-2\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(x+3\right)\left[x-3-2\left(x+3\right)\right]=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-3-2x-6\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(-x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-9\end{matrix}\right.\)
b) \(x^3-3x^2+3x-1=0\)
\(\Leftrightarrow x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3=0\)
\(\Leftrightarrow\left(x-1\right)^3=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
d) \(x^2-8x+3x-24=0\)
\(\Leftrightarrow\left(x^2-8x\right)+\left(3x-24\right)=0\)
\(\Leftrightarrow x\left(x-8\right)+3\left(x-8\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x-8=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=8\end{matrix}\right.\)
1 tháng 9 2023
a) \(x^2-9=2\left(x+3\right)^2\)
\(\Leftrightarrow\left(x+3\right)\left(x-3\right)=2\left(x+3\right)^2\)
\(\Leftrightarrow2\left(x+3\right)^2-\left(x+3\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left[2\left(x+3\right)-\left(x-3\right)\right]=0\)
\(\Leftrightarrow\left(x+3\right)\left[2x+6-x+3\right]=0\)
\(\Leftrightarrow\left(x+3\right)\left(x+9\right)=0\)
\(\)\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x+9=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-9\end{matrix}\right.\)
b) \(x^2-8x+3x-24=0\)
\(\Leftrightarrow\left(x-8\right)x+3\left(x-8\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x+3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-3\end{matrix}\right.\)
c) \(x^3-3x^2+3x-1=0\)
\(\Leftrightarrow\left(x-1\right)^3=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
TH
4
TM
21 tháng 7 2016
áp dụng các hằng đẳng thức thôi mà :)
a)\(x^2-2x+1=25\)
=>\(\left(x-1\right)^2=25\)
=>\(\orbr{\begin{cases}x-1=-5\\x-1=5\end{cases}}\)
b)\(3\left(x-1\right)^2-3x\left(x-5\right)=1\)
=>\(3\left[\left(x-1\right)^2-x\left(x-5\right)\right]=1\)
=>\(3\left(x^2-2x+1-x^2+5x\right)=1\)
=>\(3\left(3x+1\right)=1\)
=>\(3x+1=\frac{1}{3}\)
=>\(3x=\frac{-2}{3}\)
=>\(x=\frac{-2}{9}\)
c)\(\left(5-2x\right)^2-16=0\)
=>\(\left(5-2x\right)^2-4^2=0\)
=>\(\left(5-2x-4\right)\left(5-2x+4\right)=0\)
=>\(\orbr{\begin{cases}5-2x-4=0\\5-2x+4=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{9}{2}\end{cases}}}\)
\(\Rightarrow x\left(x^2-0,25\right)=0\\ \Rightarrow x\left(x-0,5\right)\left(x+0,5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=0,5\\x=-0,5\end{matrix}\right.\)