The sum of a positive number and its square is 272. What is the number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16
If the number is \(n\), then \(n+n^{2}=n(n+1)\), the product of two consecutive numbers. So 272 has to be split into two consecutive factors.
\(n^{2}+n=272\), so \(n(n+1)=272\)
\(272=16\times17\)
The number is positive, so \(n=16\)
Check: \(16+256=272\)
The number is 16.