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x_1^2 + x_2^2 = 5 if x^2 - bx + c = 0 has 2 real roots

Source: 2009 Puerto Rico Team Selection Test p4

October 23, 2021
algebratrinomialquadratic polynomial

Problem Statement

Find all integers b b and c c such that the equation x2−bx+c=0 x^2 - bx + c = 0 has two real roots x1,x2 x_1, x_2 satisfying x12+x22=5 x_1^2 + x_2^2 = 5.
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