Toán Lớp 8: Giải x
x(x–1)= 2
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Toán Lớp 8: Giải x
x(x–1)= 2
giải chi tiết ạ
Comments ( 2 )
Answer
x . (x – 1) = 2
=> x^2 – x = 2
=> x^2 – x – 2 = 0
=> x^2 – 2x + x – 2 = 0
=> (x^2 – 2x) + (x – 2) = 0
=> x . (x – 2) + (x – 2) = 0
=> (x + 1) . (x – 2) = 0
=> $\left[\begin{matrix} x + 1 = 0\\ x – 2 = 0\end{matrix}\right.$
=> $\left[\begin{matrix} x = 0 – 1\\ x = 0 + 2\end{matrix}\right.$
=> $\left[\begin{matrix} x = – 1\\ x = 2\end{matrix}\right.$
Vậy x \in {-1 ; 2}
x ( x – 1 ) = 2
⇔ x . x – x . 1 = 2
⇔ x² – x = 2
⇔ x² – x – 2 = 0
⇔ x² – ( 2x – x ) – 2 = 0
⇔ x² – 2x + x – 2 = 0
⇔ ( x² – 2x ) + ( x – 2 ) = 0
⇔ x ( x – 2 ) + ( x – 2 ) = 0
⇔ ( x + 1 ) ( x – 2 ) = 0
⇔ $\left[\begin{matrix} x + 1 = 0 \\ x – 2 = 0 \end{matrix}\right.$
⇔ $\left[\begin{matrix} x = -1 \\ x = 2 \end{matrix}\right.$
Vậy x = -1 hoặc x = 2