10.8

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(2)

select non consecutives from no: 1-11 (V Soros Olympiad 1998-99 Round 1 10.8)

Source:

In how many ways can you choose several numbers from the numbers

1,2,3,..., 11

so that among the selected numbers there are not three consecutive numbers?

combinatoricsnumber theory

ax^2+bx+c<1=1/\sqrt{1-x^2} (V Soros Olympiad 1998-99 Round 3 10.8)

Source:

It is known that for all

x

|x| < 1

, the following inequality holds

ax^2+bx+c\le \frac{1}{\sqrt{1-x^2}}

Find the greatest value of

a + 2c

inequalitiesalgebra