Show that if x^2 – 5x + 6 = 0, then x = 3 or x = 2 - Vidyadip

Question

Show that if $x^2 – 5x + 6 = 0$, then $x = 3$ or $x = 2$

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Answer

$x^{2}-5 x+6=0 \text { (given) }$
$\Rightarrow (x – 3) (x – 2) = 0 ($replacing an expression by an equal/equivalent expression$) \Rightarrow x – 3 = 0$ or $x – 2 = 0 ($from the established theorem $ab = 0 \Rightarrow $ either $a = 0 $ or $b = 0,$ for $a, b$ in $R)$
$\Rightarrow x – 3 + 3 = 0 + 3 $ or $x – 2 + 2 = 0 + 2 ($adding equal quantities on either side of the equation does not alter the nature of the equation$)$
$\Rightarrow x + 0 = 3$ or $x + 0 = 2 ($using the identity property of integers under addition$)$
$\Rightarrow x = 3$ or $x = 2 ($using the identity property of integers under addition$)$
Hence, $x^2– 5x + 6 = 0$ implies $x = 3$ or $x = 2$

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