Question

One number is the square of another. their sum is 182. find the numbers.

Answer 1

$n-first\ number\\n^2-second\ number\\\\\text{The equation:}\\\\n+n^2=182\qquad\text{subtract 182 from both sides}\\\\n^2+n-182=0\\\\n^2+14n-13n-182=0\\\\n(n+14)-13(n+14)=0\\\\(n+14)(n-13)=0\iff n+14=0\ \vee\ n-13=0\\\\\boxed{n=-14\ or\ n=13}\\\\n^2=(-14)^2=196\ ot\ n^2=13^2=169\\\\Answer:\ \boxed{196\ and\ -14\ or\ 169\ and\ 13}$