Giải các phương trình: `a)` `x“(x – 2)` `=` `x“(2x + 1)` `b)` `x/2“(x – 2)` `=` `(x – 2)“(3x + 1)`

a)

x(x – 2) = x(2x + 1)

<=> x(x – 2) – x(2x + 1) = 0

<=> x[x – 2 – (2x + 1)] = 0

<=> x(x – 2 – 2x – 1) = 0

<=> x(-x – 3) = 0

<=> -x(x + 3) = 0

<=> $\left[\begin{matrix} -x = 0\\ x + 3 = 0\end{matrix}\right.$ <=> $\left[\begin{matrix} x = 0\\ x = -3\end{matrix}\right.$

Vậy S = {0; -3}

b)

x/2(x – 2) = (x – 2)(3x + 1)

<=> x/2(x – 2) – (x – 2)(3x + 1) = 0

<=> [x – 2][x/2 – (3x + 1)] = 0

<=> (x – 2)(x/2 – 3x – 1) = 0

<=> (x – 2)(-(5x)/2 – 1) = 0

<=> $\left[\begin{matrix} x – 2 = 0\\ -\dfrac{5x}{2} – 1 = 0\end{matrix}\right.$ <=> $\left[\begin{matrix} x = 2\\ x = -\dfrac{2}{5}\end{matrix}\right.$

Vậy S = {2; -2/5}