Đáp án+Giải thích các bước giải:
`a.`
`x^2-4x=0`
`<=>x.(x-4)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\x-4=0\end{array} \right .\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=4\end{array} \right .\)
Vậy `x=0` hoặc `x=4`
`b.`
`3x(x-2021)-x+2021=0`
`<=>3x(x-2021)-(x-2021)=0`
`<=>(3x-1).(x-2021)=0`
`<=>`\(\left[ \begin{array}{l}3x-1=0\\x-2021=0\end{array} \right .\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{3}\\x=2021\end{array} \right .\)
Vậy `x=1/3` hoặc `x=2021`
`c.`
`4x(x+1)=8x(x+1)`
`<=>4x(x+1)-8x(x+1)=0`
`<=>(x+1).(4x-8x)=0`
`<=>(x+1).(-4x)=0`
`<=>`\(\left[ \begin{array}{l}x+1=0\\-4x=0\end{array} \right .\)
`<=>`\(\left[ \begin{array}{l}x=-1\\x=0\end{array} \right .\)
Vậy `x=-1` hoặc `x=0`
`d.`
`2x(x-1)-3(1-x)=0`
`<=>2x(x-1)+3(x-1)=0`
`<=>(2x+3)(x-1)=0`
`<=>`\(\left[ \begin{array}{l}2x+3=0\\x-1=0\end{array} \right .\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{-3}{2}\\x=1\end{array} \right .\)
Vậy `x=-3/2` hoặc `x=1`
`e.`
`4x^2-49=0`
`<=>(2x)^2-7^2=0`
`<=>(2x-7).(2x+7)=0`
`<=>`\(\left[ \begin{array}{l}2x-7=0\\2x+7=0\end{array} \right .\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{7}{2}\\x=\dfrac{-7}{2}\end{array} \right .\)
Vậy `x=7/2` hoặc `x=-7/2`
Áp dụng `a^2-b^2=(a-b).(a+b)`
`f.`
`x^2+36=12x`
`<=>x^2-12x+36=0`
`<=>x^2-2.6.x+6^2=0`
`<=>(x-6)^2=0`
`<=>x-6=0`
`<=>x=6`
Vậy `x=6`
Áp dụng: `a^2-2ab+b^2=(a-b)^2`
`i.`
`(1)/(16)x^2+4=x`
`<=>(1)/(16)x^2-x+4=0`
`<=>((1)/(4).x)^2-2.(1)/(4)x.2+2^2=0`
`<=>((1)/(4)x-2)^2=0`
`<=>(1)/(4)x-2=0`
`<=>(1)/(4)x=2`
`<=>x=2:(1)/(4)`
`<=>x=8`
Vậy `x=8`
Áp dụng: `a^2-2ab+b^2=(a-b)^2`
`k.`
`x^3-x^2-x+1=0`
`<=>x^2(x-1)-(x-1)=0`
`<=>(x^2-1).(x-1)=0`
`<=>(x-1).(x+1).(x-1)=0`
`<=>(x+1).(x-1)^2=0`
`<=>`\(\left[ \begin{array}{l}x+1=0\\x-1=0\end{array} \right .\)
`<=>`\(\left[ \begin{array}{l}x=-1\\x=1\end{array} \right .\)
Vậy `x=-1` hoặc `x=1`
Áp dụng: `a^2-b^2=(a-b).(a+b)`
