Question

Solve the following quadratic equations by factorization method:
$3x-\frac{8}{x}=2$

• A. $\{-\frac{4}{3},2\}$
• B. $\{-\frac{4}{3},-2\}$
• C. $\{\frac{4}{3},2\}$
• D. None of these

Answer 1

The correct option is A $\{-\frac{4}{3},2\}$

$3x-\frac{8}{x}=2$

$\Rightarrow$ $3x^2-8=2x$ [ Multiplying both sides by $x$ ]

$\Rightarrow$ $3x^2-2x-8=0$

$\Rightarrow$ $3x^2-6x+4x-8=0$

$\Rightarrow$ $3x(x-2)+4(x-2)=0$

$\Rightarrow$ $(x-2)(3x+4)=0$

$\Rightarrow$ $x-2=0$ and $3x+4=0$

$\therefore$ $x=2$ and $x=-\frac{4}{3}$