MathDB

System of equations

Source: Moldova TST 2011, day 2, problem 2

March 8, 2011

quadraticsalgebrapolynomialcomplex numbersalgebra unsolved

Problem Statement

Find all pairs of real number

x

and

y

which simultaneously satisfy the following 2 relations:

x+y+4=\frac{12x+11y}{x^2+y^2}

y-x+3=\frac{11x-12y}{x^2+y^2}