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Question

Two number differ by 3 and their product is 504. Find the number

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Solution

Let the two numbers be x and y
x-y = 3 ..... i)
and xy=504 ....ii)
Then from i)
x = y+3 .... iii)
Putting the value of iii) in ii)
left parenthesis y plus 3 right parenthesis y equals 504 y squared plus 3 y minus 504 equals 0 y squared plus 24 x minus 21 x minus 504 equals 0 y left parenthesis y plus 24 right parenthesis minus 21 left parenthesis x plus 24 right parenthesis equals 0 left parenthesis y minus 21 right parenthesis left parenthesis y plus 24 right parenthesis equals 0 y equals 21 space o r space minus 24

As it is not mentioned that the number is positive or negative so both then values can be recognised.
Hence if one number is 24 then the other number is 24-3=21, and
If one number is -21 then the other number is -21-3= -24

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