Đáp án:
a) `3(x - 1) ( 2x - 1) = 5(x + 8) (x - 1)`
`<=>` ` 3(x - 1) ( 2x - 1) - 5(x + 8) (x - 1) = 0`
`<=>` `( x - 1 )[ 3( 2x - 1 ) - 5( x + 8 ) ] = 0 `
`<=>` `( x - 1 ) ( 6x - 3 - 5x - 40 ) = 0 `
`<=>` `( x - 1 )( x - 43 ) = 0`
`<=>` \(\left[ \begin{array}{l}x-1=0\\x-43=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=1\\x=43\end{array} \right.\)
b) `9x^2 - 1 = ( 3x + 1) (4x+1)`
`<=>`` ( 3x + 1 )( 3x - 1 ) - ( 3x + 1) (4x+1) = 0`
`<=>`` ( 3x + 1 )( 3x - 1 - 4x - 1 ) = 0`
`<=>`` ( 3x + 1 )( -2 - x ) = 0`
`<=>` \(\left[ \begin{array}{l}3x+1=0\\-2-x=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\frac{-1}{3}\\x=-2\end{array} \right.\)
c) `(x + 7) (3x - 1) = 49 - x^2`
`<=>` `(x + 7) (3x - 1) - ( 7 - x )( x + 7 ) = 0 `
`<=>` `( x + 7 )( 3x - 1 - 7 + x ) = 0`
`<=>`` ( x+ 7 )( 4x - 8 ) = 0 `
`<=>`\(\left[ \begin{array}{l}x + 7=0\\4x-8=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-7\\x=2\end{array} \right.\)
d) `( 2x + 1)^2 = ( x - 1)^2`
`<=>`` ( 2x + 1 + x - 1 )( 2x + 1 -x + 1 ) = 0`
`<=>`` 3x( x+ 2 ) = 0`
`<=>`\(\left[ \begin{array}{l}3x=0\\x+2=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=0\\x=-2\end{array} \right.\)
e) `x^3 - 5x^2 + 6x = 0`
`<=>` `x( x^2 - 5x + 6 ) = 0`
`<=>` `x( x² - 2x -3x + 6 ) = 0`
`<=>` `x[ x( x - 2) - 3( x - 2 ) ] = 0`
`<=>` `x( x - 2 )( x - 3 ) = 0`
`<=>` $\left[\begin{matrix} x=0\\x - 2 =0\\ x - 3 =0 \end{matrix}\right.$
`<=>` $\left[\begin{matrix} x=0\\x = 2 \\ x = 3 \end{matrix}\right.$
g) `2x^3 + 3x^2 = 32x - 48`
Đề câu g sai =)))
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