tìm x biết
a. x(x-1)=0
b. $3x^{2}$ -6x=0
c. x(x-6)+10(x-6)=0
d. $x^{3}$ -x=0
e.3x(x-10)=x-10
f.x(x+7)= 4x+48
tìm x biết
a. x(x-1)=0
b. $3x^{2}$ -6x=0
c. x(x-6)+10(x-6)=0
d. $x^{3}$ -x=0
e.3x(x-10)=x-10
f.x(x+7)= 4x+48
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}`
——————
`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}`
——————
`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}`
——————
`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}`
——————
`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}`
——————
`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