MathDB

1

Part of 2011 Bosnia And Herzegovina - Regional Olympiad

Problems(3)

Regional Olympiad - FBH 2011 Grade 9 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

9/26/2018
Factorise (a+2b−3c)3+(b+2c−3a)3+(c+2a−3b)3(a+2b-3c)^3+(b+2c-3a)^3+(c+2a-3b)^3
factorizationalgebra
Regional Olympiad - FBH 2011 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

9/26/2018
Find the real number coefficient cc of polynomial x2+x+cx^2+x+c, if his roots x1x_1 and x2x_2 satisfy following: 2x132+x2+2x232+x1=−1\frac{2x_1^3}{2+x_2}+\frac{2x_2^3}{2+x_1}=-1
algebrapolynomial
Regional Olympiad - FBH 2011 Grade 11 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

9/26/2018
Determine value of real parameter λ\lambda such that equation 1sin⁡x+1cos⁡x=λ\frac{1}{\sin{x}} + \frac{1}{\cos{x}} = \lambda has root in interval (0,π2)\left(0,\frac{\pi}{2}\right)
parameterizationalgebra