MathDB

5

Part of 2015 South East Mathematical Olympiad

Problems(2)

Range of values

Source: China Southeast Math Olympiad 2015 Day 2 P5

6/6/2017
Suppose that a,ba,b are real numbers, function f(x)=ax+bf(x) = ax+b satisfies ∣f(x)∣≤1\mid f(x) \mid \leq 1 for any x∈[0,1]x \in [0,1]. Find the range of values of S=(a+1)(b+1).S= (a+1)(b+1).
algebra
2015 China South East MO Grade 11 P5

Source: 2015 China South East MO Grade 11 P5

1/16/2018
Given two points EE and FF lie on segment ABAB and ADAD, respectively. Let the segments BFBF and DEDE intersects at point CC. If it’s known that AE+EC=AF+FCAE+EC=AF+FC, show that AB+BC=AD+DCAB+BC=AD+DC.
geometry