A positive number added to its own square gives 342. Find the number.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 18
If the number is \(n\), then \(n+n^{2}=n(n+1)\), the product of two consecutive numbers. So 342 has to be split into two consecutive factors.
\(n^{2}+n=342\), so \(n(n+1)=342\)
\(342=18\times19\)
The number is positive, so \(n=18\)
Check: \(18+324=342\)
The number is 18.
Why the other options are incorrect
Option (1) 19 — Incorrect. \(19+19^{2}=19+361=380\), not 342.
Option (2) 21 — Incorrect. \(21+21^{2}=21+441=462\), not 342.
Option (4) 17 — Incorrect. \(17+17^{2}=17+289=306\), not 342.