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Question
The sum of a natural number and its square is 156. Find the number.
Solution
Let the required natural number be x.
According to the given condition,
`x+x^2=156`
⇒`x^2+x-156=0`
⇒`x^2+13x-12x-156=0`
⇒`x(x+13)-12(x+13)=0`
⇒`(x+13)(x-12)=0`
⇒`x+13=0 or x-12=0`
⇒`x=-13 or x=12`
∴`x=12` (x cannot be negative)
Hence, the required natural number is 12.
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