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9.3

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(3)

R(x - 1)^2+ y^2} +R{x^2 + (y -1)^2} = R2 (V Soros Olympiad 1998-99 Round 1 9.3)

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5/25/2024
On the coordinate plane, draw a set of points M(x;y)M(x;y), whose coordinates satisfy the equation (x−1)2+y2+x2+(y−1)2=2.\sqrt{(x - 1)^2+ y^2} +\sqrt{x^2 + (y -1)^2} = \sqrt2.
algebraanalytic geometry
floor + fractional parts 3x3 system (V Soros Olympiad 1998-99 Round 2 9.3)

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5/25/2024
Solve the system of equations: {x+[y]+{z}=3.9y+[z]+{x}=3.5z+[x]+{y}=2.\begin{cases} x + [y] + \{z\}=3.9 \\ y + [z] + \{x\}= 3.5 \\ z + [x] + \{y\}= 2. \end{cases}
system of equationsfractional partalgebra
3x2 non linear system (V Soros Olympiad 1998-99 Round 3 9.3)

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5/25/2024
Solve the system of equations: x−1xy−3=y−2xy−4=3−x−y7−x2−y2\frac{x-1}{xy-3}=\frac{y-2}{xy-4}=\frac{3-x-y}{7-x^2-y^2}
algebrasystem of equations