Mathematics
The product of the digits of a two digit number is 24. If it's unit's digits exceeds twice it's ten's digit by 2; find the number.
Quadratic Equations
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Answer
Let unit's digit be x and ten's digit be y.
According to question,
⇒ xy = 24 ……..(i)
⇒ x = 2y + 2 ……..(ii)
Substituting value of x from (ii) in (i) we get,
⇒ (2y + 2)y = 24
⇒ 2y2 + 2y = 24
⇒ y2 + y = 12
⇒ y2 + y - 12 = 0
⇒ y2 + 4y - 3y - 12 = 0
⇒ y(y + 4) - 3(y + 4) = 0
⇒ (y - 3)(y + 4) = 0
⇒ y - 3 = 0 or y + 4 = 0
⇒ y = 3 or y = -4.
Since digit at ten's place cannot be negative
∴ y ≠ -4.
⇒ x = 2y + 2 = 2(3) + 2 = 8
Number = 10(y) + x = 10(3) + 8 = 38.
Hence, number = 38.
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