MathDB

17

Part of 2015 BMT Spring

Problems(2)

2015 BMT Team 17

Source:

1/6/2022
There exist real numbers xx and yy such that x(a3+b3+c3)+3yabc≥(x+y)(a2b+b2c+c2a)x(a^3 + b^3 + c^3) + 3yabc \ge (x + y)(a^2b + b^2c + c^2a) holds for all positive real numbers a,ba, b, and cc. Determine the smallest possible value of x/yx/y. .
algebra
area if union circle and square, AE + AF = 2(BE + DF) 2015 BMT Individual 17

Source:

1/3/2022
A circle intersects square ABCDABCD at points A,EA, E, and FF, where EE lies on ABAB and FF lies on ADAD, such that AE+AF=2(BE+DF)AE + AF = 2(BE + DF). If the square and the circle each have area 1 1, determine the area of the union of the circle and square.
geometryareassquare