MathDB

4

Part of 2009 Puerto Rico Team Selection Test

Problems(2)

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

10/23/2021
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.
algebratrinomialquadratic polynomial
<MAB=<MCB iff <MBA=<MDA, ABCD # Puerto Rico Ibero IMO TST 2009.4

Source:

9/16/2021
The point M M is chosen inside parallelogram ABCD ABCD. Show that ∠MAB \angle MAB is congruent to ∠MCB \angle MCB, if and only if ∠MBA \angle MBA and ∠MDA \angle MDA are congruent.
geometryequal anglesparallelogram