Giải toán 8 tập 1: Câu 81 sgk trang 33

a) \(\dfrac{2}{3}x(x^2 - 4) = 0\)
\(\Leftrightarrow \dfrac{2}{3}x(x - 2) (x + 2) = 0\)
\(\Leftrightarrow x(x - 2) (x + 2) = 0\)
\(\Leftrightarrow \left[\begin{array}{l} x = 0 \\ x - 2 = 0 \\ x + 2 = 0\end{array} \right.\\ \\ \Leftrightarrow \left[\begin{array}{l}x = 0 \\ x = 2 \\ x = -2\end{array} \right.\)
b) \((x + 2)^2 - (x - 2)(x + 2) = 0\)
\(\Leftrightarrow (x + 2) [(x + 2) - (x - 2)] = 0\)
\(\Leftrightarrow (x + 2) (x + 2 - x + 2) = 0\)
\(\Leftrightarrow (x + 2).4 = 0\)
\(\Leftrightarrow x + 2 = 0\)
\(\Leftrightarrow x = -2\)
c) \(x + 2\sqrt{2}x^2 + 2x^3 = 0\)
\(\Leftrightarrow x (1 + 2\sqrt{2}x + 2x^2) = 0\)
\(\Leftrightarrow x(1 + \sqrt{2}x)^2 = 0\)
\(\Leftrightarrow \left[\begin{array}{l} x = 0 \\ 1 + \sqrt{2}x = 0\end{array} \right.\\\\\Leftrightarrow \left[\begin{array}{l} x = 0 \\ x = - \dfrac{1}{\sqrt{2}} =- \dfrac{\sqrt{2}}{2} \end{array} \right.\)