MathDB

7

Part of 2020 LIMIT Category 1

Problems(2)

LIMIT 2020 P7

Source: LIMIT 2020

4/11/2020
△ABC\triangle{ABC} is equailateral. EE is any point on AC‾\overline{AC} produced and the equilateral △ECD\triangle{ECD} is drawn. If MM and NN are the midpoints of AD‾\overline{AD} and EB‾\overline{EB} respectively then show that △CMN\triangle{CMN} is equilateral.
geometrytrapezoidgeometric transformation
Exploiting Vieta's relations

Source: LIMIT 2020 Cat 1 Obj P7

5/2/2020
Let P(x)=x6−x5−x3−x2−xP(x)=x^6-x^5-x^3-x^2-x and a,b,ca,b,c and dd be the roots of the equation x4−x3−x2−1=0x^4-x^3-x^2-1=0, then determine the value of P(a)+P(b)+P(c)+P(d)P(a)+P(b)+P(c)+P(d)
(A)55 (B)66 (C)77 (D)88
algebrapolynomiallimitVieta