a) \(\left(x+1\right)^2=3\left(x+1\right)\)
\(\Leftrightarrow\left(x+1\right)^2-3\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)
b) \(\left(2x-7\right)^3=8\left(7-2x\right)^2\)
\(\Leftrightarrow\left(2x-7\right)^3-8\left(2x-7\right)^2=0\)
\(\Leftrightarrow\left(2x-7\right)^2\left(2x-15\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(2x-7\right)^2=0\\2x-15=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=7\\2x=15\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=\frac{15}{2}\end{cases}}\)
a, \(\left(x+1\right)^2=3\left(x+1\right)\Leftrightarrow x^2+2x+1=3x+3\)
\(\Leftrightarrow x^2-x-2=0\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\Leftrightarrow\orbr{\begin{cases}x=-2\\x=1\end{cases}}\)
b, \(\left(2x-7\right)^3=8\left(7-2x\right)^2\)
\(\Leftrightarrow8x^3-116x^2+518x-735=0\Leftrightarrow\orbr{\begin{cases}x=3,5\\x=7,5\end{cases}}\)
a) (x + 1)2 = 3(x + 1)
<=> x2 + 2x + 1 = 3x + 3
<=> x2 - x - 2 = 0
<=> x2 - 2.1/2 .x + 1/4 - 9/4 = 0
<=> (x - 1/2)2 = 9/4
<=> x - 1/2 = \(\sqrt{\frac{9}{4}}\)
<=> x = 3/2 + 1/2 = 2
vậy pt có nghiệm x = 2
( x + 1 )2 = 3( x + 1 )
<=> x2 + 2x + 1 = 3x + 3
<=> x2 + 2x + 1 - 3x - 3 = 0
<=> x2 - x - 2 = 0
<=> x2 - 2x + x - 2 = 0
<=> x( x - 2 ) + 1( x - 2 ) = 0
<=> ( x - 2 )( x + 1 ) = 0
<=> x = 2 hoặc x = -1
( 2x - 7 )3 = 8( 7 - 2x )2
<=> ( 2x - 7 )3 = 8( 2x - 7 )2
<=> ( 2x - 7 )3 - 8( 2x - 7 )2 = 0
<=> ( 2x - 7 )2( 2x - 7 - 8 ) = 0
<=> x = 7/2 hoặc x = 15/2
