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A system of equation with squares/roots for real numbers

Source: 2017 Azerbaijan Junior/Senior National Olympiad

April 28, 2022
system of equationsalgebra

Problem Statement

Solve the system of equation for (x,y)∈R(x,y) \in \mathbb{R} {x2+y2+(x−4)2+(y−3)2=53x2+4xy=24\left\{\begin{matrix} \sqrt{x^2+y^2}+\sqrt{(x-4)^2+(y-3)^2}=5\\ 3x^2+4xy=24 \end{matrix}\right. \\ Explain your answer
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