Question

[Trịnh Hải Nam]

The sum of all possible natural number n such that : n²+n+1589 is a perfect square is

Answer 1

[Việt Nguyễn Đức]

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Answer 2

[Việt Nguyễn Đức]

\(^{n^{ }2}\)+n+1589

=( \(^{n^{ }2}\)+n+\(\dfrac{1}{4}\))+\(\dfrac{6355}{4}\)

=(n+\(\dfrac{1}{2}\))^2+\(\dfrac{6355}{4}\)

Đặt n+\(\dfrac{1}{2}\)= a => \(a^2\)+\(\dfrac{6355}{4}\)=\(b^2\)

Tự giải a sau đó suy ra n=a -\(\dfrac{1}{2}\)