Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2 - Vidyadip

Question

Show that if x² – 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) ⇒ x – 3 = 0 or x – 2 = 0 (from the established theorem ab = 0 ⇒ 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, x²– 5x + 6 = 0 implies x = 3 or x = 2

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