Đáp án:
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Giải thích các bước giải:
`a)`
`4x(x-5)-(x-1)(4x-3)=10`
`⇔4x²-20x-(4x²-3x-4x+3)=10`
`⇔4x²-20x-4x²+3x+4x-3=10`
`⇔(4x²-4x²)-(20x-3x-4x)-3=10`
`⇔-13x-3=10`
`⇔-13x=10+3`
`⇔-13x=13`
`⇔x=13:(-13)`
`⇔x=-1`
Vậy `x=-1`
`b)`
`(2x-1)(x-2)-(x+3)(2x-7)=3`
`⇔2x²-4x-x+2-(2x²-7x+6x-21)=3`
`⇔2x²-4x-x+2-2x²+7x-6x+21=3`
`⇔(2x²-2x²)+(-4x-x+7x-6x)+(2+21)=3`
`⇔-4x+23=3`
`⇔-4x=3-23`
`⇔-4x=-20`
`⇔x=(-20):(-4)`
`⇔x=5`
Vậy `x=5`
`c)`
`(x+3)(x-4)+(x-1)(x+1)=10`
`⇔x²-4x+3x-12+x²-1-10=0`
`⇔(x²+x²)+(-4x+3x)-(12+1+10)=0`
`⇔2x²-x-23=0`
`⇔2(x²-1/2x-23/2)=0`
`⇔x²-1/2x-23/2=0`
`⇔x²-1/2x+1/16-185/16=0`
`⇔x²-1/2x+1/16=185/16`
`⇔x²-2.x. 1/4+(1/4)^2=185/16`
`⇔(x-1/4)^2=(`$\dfrac{\sqrt{185}}{4}$`)^2`
`⇔`$\left[\begin{matrix} x-\dfrac{1}{4}=\dfrac{\sqrt{185}}{4}\\ x-\dfrac{1}{4}=-\dfrac{\sqrt{185}}{4}\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=\dfrac{\sqrt{185}}{4}+\dfrac{1}{4}\\ x=-\dfrac{\sqrt{185}}{4}+\dfrac{1}{4}\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=\dfrac{\sqrt{185}+1}{4}\\ x=\dfrac{1-\sqrt{185}}{4}\end{matrix}\right.$
Vậy `x\in{`$\dfrac{\sqrt{185}+1}{4}$`;`$\dfrac{1-\sqrt{185}}{4}$`}`
`d)`
`8x(x-3)-8(x-1)(x+1)=20`
`⇔8x²-24x-8(x²-1)=20`
`⇔8x²-24x-8x²+8=20`
`⇔(8x²-8x²)-24x+8=20`
`⇔-24x+8=20`
`⇔-24x=20-8`
`⇔-24x=12`
`⇔x=-12/24`
`⇔x=-1/2`
Vậy `x=-1/2`
