Answer
{$1,3$}
Work Step by Step
Step 1: Comparing $x^{2}-4x+3=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=1$, $b=-4$ and $c=3$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt (b^{2}-4ac)}{2a}$
Step 3: Substituting the values of a,b and c in the formula:
$x=\frac{-(-4) \pm \sqrt ((-4)^{2}-4(1)(3))}{2(1)}$
Step 4: $x=\frac{4 \pm \sqrt (16-12)}{2}$
Step 5: $x=\frac{4 \pm \sqrt (4)}{2}$
Step 6: $x=\frac{4 \pm2}{2}$
Step 7: $x=\frac{4+2}{2}$ or $x=\frac{4-2}{2}$
Step 8: $x=\frac{6}{2}$ or $x=\frac{2}{2}$
Step 9: $x=3$ or $x=1$
Step 10: Therefore, the solution set is {$1,3$}.
