Giai các phương trình :
a) \(2x+5=20-3x\)
\(\Leftrightarrow2x+3x=20-5\)
\(\Leftrightarrow5x=15\)
\(\Leftrightarrow x=3\)
Vậy : \(S=\left\{3\right\}\)
b) \(\left(2x-1\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(2x-1+x+3\right)\left(2x-1-x-3\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+2=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{-2}{3}\\x=4\end{matrix}\right.\)
Vậy : \(S=\left\{\frac{-2}{3};4\right\}\)
c) \(\frac{5x-4}{2}=\frac{16x+1}{7}\)
\(\Leftrightarrow35x-28=32x+2\)
\(\Leftrightarrow3x=30\)
\(\Leftrightarrow x=10\)
Vậy : \(S=\left\{10\right\}\)
c)\(\frac{5x-4}{2}=\frac{16x+1}{7}\)
\(\Leftrightarrow7\left(5x-4\right)=2\left(16x+1\right)\)
\(\Leftrightarrow35x-28=32x+2\)
\(\Leftrightarrow35x-32x=2+28\)
\(\Leftrightarrow3x=30\)
\(\Leftrightarrow x=10\)
Vậy phương trình có nghiệm là: x = 10
a) \(2x+5=20-3x\)
\(\Leftrightarrow2x+3x=20-5\)
\(\Leftrightarrow5x=15\)
\(\Leftrightarrow x=3\)
Vậy phương trình có nghiệm là: x = 3
b) \(\left(2x+1\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(4x^2-4x+1\right)-\left(x^2+6x+9\right)=0\)
\(\Leftrightarrow4x^2+4x+1-x^2-6x-9=0\)
\(\Leftrightarrow3x^2-2x-8=0\)
\(\Leftrightarrow3x^2-\left(6x-4x\right)-8=0\)
\(\Leftrightarrow\left(3x^2-6x\right)+\left(4x-8\right)=0\)
\(\Leftrightarrow3x\left(x-2\right)+4\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x+4\right)=0\)
\(\Leftrightarrow x-2=0hoặc3x+4=0\)
* TH1: x - 2=0
\(\Leftrightarrow x=0+2\)
\(\Leftrightarrow x=2\)
* TH2 : 3x + 4 = 0
\(\Leftrightarrow3x=-4\)
\(\Leftrightarrow x=\frac{-4}{3}\)
Vậy phương trình có nghiệm là: x = 2 và x = \(\frac{-4}{3}\)
Sửa lại phần b
b)\(\left(2x-1\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow4x^2-4x+1-x^2-6x-9=0\)
\(\Leftrightarrow3x^2-10x-8=0\)
\(\Leftrightarrow\left(3x-12\right)+\left(2x-8\right)=0\)
\(\Leftrightarrow3x\left(x-4\right)+2\left(x-4\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left(x-4\right)=0\)
\(\Leftrightarrow3x+2=0hoặcx-4=0\)
*TH1: 3x + 2 = 0
\(\Leftrightarrow3x=-2\)
\(\Leftrightarrow x=\frac{-2}{3}\)
*TH2: x - 4 = 0
\(\Leftrightarrow x=4\)
Vậy phương trình có nghiệm là : \(x=\frac{-2}{3}\); \(x=4\)
