Show that $x^{2} - 3 x + 2 = 0$ implies that $x = 1$ or $x = 2$ .

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Solution

Solving the quadratic equation, we have
$x^{2} - 3 x + 2 = 0$
$x^{2} - 2 x - x + 2 = 0$
$x (x - 2) - 1 (x - 2) = 0$
$(x - 2) (x - 1) = 0$
$x = 1, 2$
$\Rightarrow x \neq - 1 or x \neq - 2$ .

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