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EGMO TST - Moldova
2023 Moldova EGMO TST
5
6(1-x)^2=\frac{1}{y},\\6(1-y)^2=\frac{1}{x}
6(1-x)^2=\frac{1}{y},\\6(1-y)^2=\frac{1}{x}
Source: Moldova EGMO TST 2023
February 4, 2023
equation
system of equations
Problem Statement
Find all pairs of real numbers
(
x
,
y
)
(x, y)
(
x
,
y
)
, that satisfy the system of equations:
{
6
(
1
−
x
)
2
=
1
y
6
(
1
−
y
)
2
=
1
x
.
\left\{\begin{matrix} 6(1-x)^2=\dfrac{1}{y} \\ \\6(1-y)^2=\dfrac{1}{x}.\end{matrix}\right.
⎩
⎨
⎧
6
(
1
−
x
)
2
=
y
1
6
(
1
−
y
)
2
=
x
1
.
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