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Đáp án:
`a)` $\left[\begin{matrix} x=0\\ x=3\\ x = -3\end{matrix}\right.$
`b)` $\left[\begin{matrix} x=\dfrac{-2}{3}\\ x=5\end{matrix}\right.$
`c) x = -1/12`
`d) ` $\left[\begin{matrix} x=3\\ y=-2\end{matrix}\right.$
Giải thích các bước giải:
`a) x^3 - 9x = 0`
`⇔ x(x^2 - 9) = 0`
`⇔ x(x - 3)(x + 3) = 0`
`⇔` $\left[\begin{matrix} x=0\\ x-3=0\\ x + 3 = 0 \end{matrix}\right.$
`⇔` $\left[\begin{matrix} x=0\\ x=3\\ x = -3\end{matrix}\right.$
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`b) 3x(x - 5) + 2x - 10 = 0`
` ⇔ 3x(x - 5) + 2(x - 5) = 0`
` ⇔ (3x + 2)(x - 5) = 0`
` ⇔ ` $\left[\begin{matrix} 3x+2=0\\ x-5=0\end{matrix}\right.$
`⇔` $\left[\begin{matrix} x=\dfrac{-2}{3}\\ x=5\end{matrix}\right.$
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`c) (2x + 1)^2 - 4x (x - 2) = 0`
`⇔ 4x^2 + 4x + 1 - 4x^2 + 8x = 0`
`⇔ 12x + 1 = 0`
` ⇔ x = -1/12`
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`d) x^2 + y^2 - 6x + 4y + 13 = 0`
` ⇔ (x^2 - 6x + 9) + (y^2 + 4y + 4) = 0`
` ⇔ (x - 3)^2 + (y + 2)^2 = 0`
` ⇔` $\left[\begin{matrix} x=3\\ y=-2\end{matrix}\right.$
