Question

Solve the following quadratic equation by factorisation.

\[6x - \frac{2}{x} = 1\]

Answer 1

\[6x - \frac{2}{x} = 1\]  

\[\Rightarrow 6 x^2 - 2 = 1x\]
\[ \Rightarrow 6 x^2 - 1x - 2 = 0\]
\[ \Rightarrow 6 x^2 - 4x + 3x - 2 = 0\]
\[ \Rightarrow 2x\left( 3x - 2 \right) + 1\left( 3x - 2 \right) = 0\]
\[ \Rightarrow \left( 3x - 2 \right)\left( 2x + 1 \right) = 0\]
\[ \Rightarrow \left( 3x - 2 \right) = 0 \text{ or } \left( 2x + 1 \right) = 0\]
\[ \Rightarrow x = \frac{2}{3} \text{ or } x = \frac{- 1}{2} \]
\[\frac{2}{3} \text{ and } \frac{- 1}{2}\] are the roots of the given quadratic equation.