Question

已知n是自然数,且n^2-17n+61是完全平方数,求n的值.

Answer 1

n^2-17n+61=n^2-18n+n+61-81=(n-9)^2+n-20;

n^2-17n+61=n^2-16n-n+61-64=(n-8)^2-n-3;

(n-9)^2+(n-9)+(n-8)=(n-8)^2;

显然,n^2-17n+61是(n-9)^2,n=20