Mathematics
Is { x : x2 - 7x + 12 = 0 } = { 3, 4 } ?
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Answer
x2 - 7x + 12 = 0
⇒ x2 - 3x - 4x + 12 = 0
⇒ (x2 - 3x) - (4x - 12) = 0
⇒ x(x - 3) - 4(x - 3) = 0
⇒ (x - 3)(x - 4) = 0
⇒ (x - 3) = 0 or (x - 4) = 0
⇒ x = 3 or x = 4
Yes, { x : x2 - 7x + 12 = 0 } = { 3, 4 }.
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