MathDB

Solve a system in real numbers.

Source: Moldova 2008 IMO-BMO Second TST Problem 1

March 29, 2008

algebra proposedalgebra

Problem Statement

Find all solutions

(x,y)\in \mathbb{R}\times\mathbb R

of the following system: \begin{cases}x^3 \plus{} 3xy^2 \equal{} 49, \\ x^2 \plus{} 8xy \plus{} y^2 \equal{} 8y \plus{} 17x.\end{cases}