Question
Solve the following equation: $a^2x^2 - 3abx + 2b^2 = 0$
✓
Answer
$a^2 x^2-3 a b x+2 b^2=0$
$ x^2-3 \frac{b}{a} x+2\left(\frac{b}{a}\right)^2=0 $
$x^2-\frac{b}{a} x-2 \frac{b}{a} x+2\left(\frac{b}{a}\right)^2=0$
$x\left(x-\frac{b}{a}\right)-2 \frac{b}{a}\left(x-\frac{b}{a}\right)=0$
$\left(x-\frac{b}{a}\right)\left(x-2 \frac{b}{a}\right)=0 $
$ \left(x-\frac{b}{a}\right)=0,\left(x-2 \frac{b}{a}\right)=0 $
$x=\frac{b}{a}, x=2 \frac{b}{a}$
$ x^2-3 \frac{b}{a} x+2\left(\frac{b}{a}\right)^2=0 $
$x^2-\frac{b}{a} x-2 \frac{b}{a} x+2\left(\frac{b}{a}\right)^2=0$
$x\left(x-\frac{b}{a}\right)-2 \frac{b}{a}\left(x-\frac{b}{a}\right)=0$
$\left(x-\frac{b}{a}\right)\left(x-2 \frac{b}{a}\right)=0 $
$ \left(x-\frac{b}{a}\right)=0,\left(x-2 \frac{b}{a}\right)=0 $
$x=\frac{b}{a}, x=2 \frac{b}{a}$
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