MathDB

14

Part of 2014 BMT Spring

Problems(2)

2014 BMT Team 14

Source:

1/6/2022
Let (x,y)(x, y) be an intersection of the equations y=4x2−28x+41y = 4x^2 - 28x + 41 and x2+25y2−7x+100y+3494=0x^2 + 25y^2 - 7x + 100y +\frac{349}{4}= 0. Find the sum of all possible values of xx.
algebra
BMT 2014 Spring - Individual 14

Source:

1/22/2022
Suppose that f(x)=xx2−2x+2f(x) = \frac{x}{x^2 - 2x + 2} and g(x1,x2,...,x7)=f(x1)+f(x2)+...+f(x7)g(x_1, x_2, ... , x_7) = f(x_1) + f(x_2) +... + f(x_7). If x1,x2,...,x7x_1, x_2,..., x_7 are non-negative real numbers with sum 55, determine for how many tuples (x1,x2,...,x7)(x_1, x_2, ... , x_7) does g(x1,x2,...,x7)g(x_1, x_2, ... , x_7) obtain its maximal value.
algebra