Đáp án+Giải thích các bước giải:
a)
`(2x + 3)(x-4)+(x-5)(x-2)=(3x-5)(x-4)`
`<=> 2x^2 - 8x + 3x - 12 + x^2 - 2x - 5x +10 = 3x^2 - 12x - 5x +20`
`<=> 3x^2 - 7x - 2 = 3x^2 - 12x +20`
`<=> -7x - 2 = -12x +20`
`<=> 5x = 22`
`<=> x = 22/5`
Vậy `S ={22/5}`
b)
`(8x -3)(3x+2)-(4x+7)(x+4)= (2x +1)(5x-1)`
`<=> 24x^2 + 16x - 9x - 6 - (4x^2 + 16x + 7x + 28)=10x^2 - 2x + 5x -1`
`<=> 24x^2 + 16x - 9x - 6 -(4x^2 + 23x + 28) = 10x^2 + 3x -1`
`<=> 24x^2 + 16x - 9x - 6 - 4x^2 - 23x - 28 = 10x^2 + 3x -1`
`<=> 20x^2 - 16x - 34 = 10x^2 + 3x -1`
`<=> 10x^2 -19x -33 =0`
`<=> 10x^2 + 11x - 30x -33 =0`
`<=> x(10x+11)-3(10x +11)=0`
`<=> ` \(\left[ \begin{array}{l}10x+11=0\\\\x-3=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac{-11}{10}\\x=3\end{array} \right.\)
Vậy `S= {-11/10; 3}`
c)
`2x^2 + 3(x - 1)(x + 1) = 5x(x + 1)`
`<=> 2x^2 + 3(x^2-1) = 5x^2 + 5x`
`<=> 2x^2 + 3x^2 - 3 = 5x^2 +5x`
`<=> -5x = 3`
`<=> x = -3/5`
Vậy `S= {-3/5}`
d)
`(8 - 5x)(x + 2) + 4(x - 2)(x + 1) = (x - 2)(x + 2)`
`<=> 8x + 16 - 5x^2 - 10x + (4x -8)(x+1) = x^2 -4`
`<=> 8x + 16 - 5x^2 - 10x + 4x^2 + 4x - 8x -8=x^2 -4`
`<=> 8-x^2 -6x = x^2 -4`
`<=> 12-2x^2 - 6x=0`
`<=> x^2 + 3x -6=0`
`<=> x = (-3+-sqrt(3^2 - 4*1*(-6)))/(2*1)`
`<=> x = (-3 + -sqrt(33))/2`
`<=>` $\begin{cases} x =\dfrac{-3+\sqrt{33}}{2}\\\\x= \dfrac{-3-\sqrt{33}}{2} \end{cases}$
Vậy $S= {\dfrac{-3+\sqrt{33}}{2}; \dfrac{-3-\sqrt{33}}{2}}$
e)
`4(x - 1)( x + 5) - (x +2)(x + 5) = 3(x - 1)(x + 2)`
`<= >(x+5)[4(x-1)-(x+2)]= 3x^2 + 6x - 3x -6`
`<=> (x+5)(4x-4-x-2) = 3x^2 +6x - 3x -6`
`<=> 3x^2 - 6x + 15x -30 = 3x^2 + 6x - 3x - 6`
`<=> 9x - 30 = 3x -6`
`<=> 6x = 24`
`<=> x =4`
Vậy `S={4}`