Các bước giải:

`a. x.(x -1) = 0`

$⇔ \left[ \begin{array}{l}x=0\\x -1=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=0\\x=1\end{array} \right.$

Vậy `S = {0; 1}`

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`b. 3x² -6x = 0`

`⇔ 3x.(x -2) = 0`

$⇔ \left[ \begin{array}{l}3x=0\\x -2=0\end{array} \right. \left[ \begin{array}{l}x=0\\x=1\end{array} \right. $

`Vậy S = {0; 2}`

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`c. x.(x -6) +10.(x -6) = 0`

`⇔ (x -6).(x +10) = 0`

$⇔ \left[ \begin{array}{l}x -6=0\\x +10=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=6\\x=-10\end{array} \right.$

Vậy `S = {6; -10}`

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`d. x³ -x = 0`

`⇔ x.(x² -1) = 0`

$⇔ \left[ \begin{array}{l}x=0\\x² -1=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=0\\x=±1\end{array} \right.$

Vậy S = {0; ±1}`

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`e. 3x.(x -10) = x -10`

`⇔ 3x.(x -10) -(x -10) = 0`

`⇔ (x -10).(3x -1) = 0`

$⇔ \left[ \begin{array}{l}x -10=0\\3x -1=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=10\\x=\dfrac{1}{3}\end{array} \right.$

Vậy `S = {10; 1/3}`

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`f. x.(x +7)= 4x +48`

`⇔ x² +7x -4x -48 = 0`

`⇔ x² +3x -48 = 0`

`⇔ (x +3/2)² -201/4 = 0`

`⇔ (x +3/2 -(\sqrt{201})/2).(x +3/2 +(\sqrt{201})/2) = 0`

$⇔ \left[ \begin{array}{l}x +3/2 -(\sqrt{201})/2=0\\x +3/2 +(\sqrt{201})/2=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=\dfrac{-3 +\sqrt{201}}{2}\\x=\dfrac{-3 -\sqrt{201}}{2}\end{array} \right.$

Vậy `S = {`$\dfrac{-3 +\sqrt{201}}{2}; \dfrac{-3 -\sqrt{201}}{2}$`}`

Đáp án:

Giải thích các bước giải:

 a) x(x - 1) = 0

=> x = 0 hoặc x - 1 = 0

=> x = 0 hoặc x = 1

b) 3x^2 - 6x = 0 => 3x(x - 2) = 0

=> 3x = 0 hoặc x - 2 = 0

=> x = 0 hoặc x = 2

c) x(x - 6) + 10(x - 6) = 0

=> (x - 6)(x + 10) = 0

=> x = 6 hoặc x = -10

d) x^3 - x = 0

=> x(x^2 - 1) = 0

=> x = 0 hoặc x^2 - 1 = 0

=> x = 0 hoặc x^2 = 1

=> x = 0 , x = 1 , x = -1

e) 3x(x - 10) = x - 10

=> 3x(x - 10) - (x - 10) = 0

=> (x - 10)(3x - 1) = 0

=> x = 10 hoặc x = 1/3

f) x(x + 7) = 4x + 48

=> x^2 + 7x - (4x + 48) = 0

=> x^2 + 7x - 4x - 48 = 0

=> x^2 + 3x - 48 = 0

=> x không thỏa mãn