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Question
The sum of two natural number is 28 and their product is 192. Find the numbers.
Solution
Let the required number be x and (28-x).
According to the given condition,
`x(28)-x=192`
⇒`28x-x^2=192`
⇒`x^2-28x+192=0`
⇒`x^2-16x-12x+192=0`
⇒`x(x-16)-12(x-16)=0`
⇒`(x-12)(x-16)=0`
⇒`x-12=0 or x-16=0`
⇒`x=12 or x=16`
when` x=12`
`28-x=28-12=16`
when `x=16`
28-x=28-16=12`
Hence, the required numbers are 12 and 16.
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