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x^2+ [y]=10, y^2+[x]=13 (II Soros Olympiad 1995-96 R1 10.4)

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June 3, 2024
system of equationsalgebrafloor functionnice

Problem Statement

Solve the system of equations {x2+[y]=10y2+[x]=13\begin{cases} x^2+ [y]=10 \\ y^2+[x]=13 \end{cases} ([x][x] is the integer part of xx, [x][x] is equal to the largest integer not exceeding xx. For example, [3,33]=3[3,33] = 3, [2]=2[2] = 2, [−3.01]=−4[- 3.01] = -4).
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