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Question
Two natural number differ by 3 and their product is 504. Find the numbers.
Solution
Let the required numbers be x and (x+3) According to the question:
`x(x+3)=504`
⇒`x^2+3x=504`
⇒`x^2+3x-504=0`
⇒`x^2+(24-24)x-504=0`
⇒`x^2+24x-24x-504=0`
⇒`x(x-24)-21(x+24)=0`
⇒`(x+24)(x-21)=0`
⇒`x+24=0 or x-21=0`
`⇒x=-24 or x=21`
If x = -24, the numbers are `-24 and{(-24+3)=-21}`
If x =21, the numbers are `21 and {(21+3)=24}`
Hence, the numbers are `(-24,-21) and (21,24)`
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