Question

Solve for x :

\[x^2 - \left( \sqrt{3} + 1 \right) x + \sqrt{3} = 0\]

Answer 1

\[x^2 - \left( \sqrt{3} + 1 \right) x + \sqrt{3} = 0\]
\[ \Rightarrow x^2 - \sqrt{3}x - x + \sqrt{3} = 0\]
\[ \Rightarrow x\left( x - \sqrt{3} \right) - 1\left( x - \sqrt{3} \right) = 0\]
\[ \Rightarrow \left( x - 1 \right)\left( x - \sqrt{3} \right) = 0\]
\[ \Rightarrow x - 1 = 0 \text{or x} - \sqrt{3} = 0\]
\[ \Rightarrow x = 1 \text{or x} = \sqrt{3}\]