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Question
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
Solution
Let these two numbers be X and Y, Y being the bigger number. Then as per the question,
X + Y = 25 .....(i)
2Y2 = 3X2 + 29 ..... (ii)
From (i), we get Y= 25 - X. Putting this in (ii), we get
2{25-X)2 = 3X2 + 29
⇒ 1250 + 2X2 -100X= 3X2 + 29
⇒ X2 + l OO X - 1221 = 0
⇒ X2 - 11 X +111X - 1221 = 0
⇒ X (X - 11) +111( X - 11) = 0
⇒ (X-11) (X+111) = 0
⇒ X can't be a negative number and hence X=11
⇒ X=11, hence Y = 14 .
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