Question
Solve the following quadratic equation by factorization.
$6x - \frac{2}{x} = 1$
$6x - \frac{2}{x} = 1$
✓
Answer
$6 x^2-2=x $
$\Rightarrow 6 x^2-x-2=0 $
$\Rightarrow 6 x^2+3 x-4 x-2=0 $
$\Rightarrow 3 x(2 x+1)-2(2 x+1)=0 $
$\Rightarrow(3 x-2)(2 x+1)=0 $
$3 x-2=0 \Rightarrow 3 x=2 \Rightarrow x=\frac{2}{3} $
$2 x+1=0 \Rightarrow 2 x=-1 \Rightarrow x=-\frac{1}{2}$
Hence, $x =\frac{2}{3}$ and $x =-\frac{1}{2}$ are roots of the equation.
$\Rightarrow 6 x^2-x-2=0 $
$\Rightarrow 6 x^2+3 x-4 x-2=0 $
$\Rightarrow 3 x(2 x+1)-2(2 x+1)=0 $
$\Rightarrow(3 x-2)(2 x+1)=0 $
$3 x-2=0 \Rightarrow 3 x=2 \Rightarrow x=\frac{2}{3} $
$2 x+1=0 \Rightarrow 2 x=-1 \Rightarrow x=-\frac{1}{2}$
Hence, $x =\frac{2}{3}$ and $x =-\frac{1}{2}$ are roots of the equation.
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