Is { $x$ : $x^{2} - 7 x + 12 = 0$ } = {3, 4} ?

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Solution

We have $x^{2} - 7 x + 12 = 0$
$=> x^{2} - 4 x - 3 x + 12 = 0$
$=> x (x - 4) - 3 (x - 4) = 0$
$=> x = 3; 4$
Hence { $x : x^{2} - 7 x + 12 = 0$ } $=$ { $3, 4$ }

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