Question:
Short-Answer Questions
Solve: $x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$
Solution:
$x^{2}-(\sqrt{3}+1) x+\sqrt{3}=0$
$\Rightarrow x^{2}-\sqrt{3} x-x+\sqrt{3}=0$
$\Rightarrow x(x-\sqrt{3})-1(x-\sqrt{3})=0$
$\Rightarrow(x-\sqrt{3})(x-1)=0$
$\Rightarrow x-\sqrt{3}=0$ or $x-1=0$
$\Rightarrow x=\sqrt{3}$ or $x=1$
Hence, 1 and $\sqrt{3}$ are the roots of the given equation.
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