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Question
The sum of two natural numbers is 8 and their product is 15., Find the numbers.
Solution
Let the required natural numbers be x and `(8-x)`
It is given that the product of the two numbers is 15
∴ `x(8-x)=15`
⇒` 8x-x^2=15`
⇒`x^2-8x+15=0`
⇒`x^2-5x-3x+15=0`
⇒`x(x-5)-3(x-5)=0`
⇒`(x-5)(x-3)`
⇒`x-5=0 or x-3=0`
⇒`x=5 or x=3`
Hence, the required numbers are 3 and 5.
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