In a 2 digit number, the digit at the units place is equal to the square of digit at the tens place. If 54 is added to the number, the digits get interchanged. Find the number. ( answer ahould be 39 )
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Step-by-step explanation:
Let the tens digit = x, and the units digit =y.
Then y = x^2 .
The original number is then 10x + x^2.
When 54 is added the new number is 10y + x (digits reversed).
Therefore 10x + x^2 + 54 = 10x^2 + x
10x^2 + x - x^2 - 10x - 54 = 0
9x^2 - 9x - 54 = 0
x^2 - x - 6 = 0 (divide throughout by 9)
(x - 3)(x + 2) = 0
Therefore x-3 = 0 or x + 2 = 0.
Therefore x = 3
Therefore y = x^2 = 9
Therefore the original number = 10x + y = 39.
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Step-by-step explanation:
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