MathDB

15

Part of 2006 AIME Problems

Problems(2)

Sequence

Source: 2006 AIME A Problem 15

3/9/2006
Given that a sequence satisfies x0=0x_0=0 and ∣xk∣=∣xk−1+3∣|x_k|=|x_{k-1}+3| for all integers k≥1,k\ge 1, find the minimum possible value of ∣x1+x2+⋯+x2006∣|x_1+x_2+\cdots+x_{2006}|.
functioninequalitiesAMCAIMEabsolute value
Aime ii - 2006/15

Source:

3/27/2006
Given that xx, yy, and zz are real numbers that satisfy: x=y2−116+z2−116 x=\sqrt{y^2-\frac{1}{16}}+\sqrt{z^2-\frac{1}{16}} y=z2−125+x2−125 y=\sqrt{z^2-\frac{1}{25}}+\sqrt{x^2-\frac{1}{25}} z=x2−136+y2−136 z=\sqrt{x^2-\frac{1}{36}}+\sqrt{y^2-\frac{1}{36}} and that x+y+z=mnx+y+z=\frac{m}{\sqrt{n}}, where mm and nn are positive integers and nn is not divisible by the square of any prime, find m+nm+n.
AMCAIMEgeometryinequalitiesarea of a triangleHeron's formulaHi