MathDB

9.1

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(3)

parentheses in 2:2 -3:3 - 4: 4-5:5 (V Soros Olympiad 1998-99 Round 1 9.1)

Source:

5/25/2024
Place parentheses in the expression 2:2−3:3−4:4−5:52:2 -3:3 - 4: 4-5:5 so that the result is a number greater than 3939.
algebra
number of letters in this phrase is (V Soros Olympiad 1998-99 Round 2 9.1)

Source:

5/25/2024
In the phrase given at the end of the condition of the problem, it is necessary to put a number (numeral) in place of the ellipsis, written in verbal form and in the required case, so that the statement formulated in it is true. Here is this phrase: “The number of letters in this phrase is...”
algebra
x^2 + ax + b = x^2 + bx + a = 0 (V Soros Olympiad 1998-99 Round 3 9.1)

Source:

5/25/2024
It is known that each of the equations x2+ax+b=0x^2 + ax + b = 0 and x2+bx+a=0x^2 + bx + a = 0 has two different roots and these four roots form an arithmetic progression in some order. Find aa and bb.
algebra