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2013 Hanoi Open Mathematics Competitions
14
x^3+1/3 y=x^2+x-4/3 and y^3+1/4 z=y^2+y -5/4 and ... (HOMC 2013 Q14)
x^3+1/3 y=x^2+x-4/3 and y^3+1/4 z=y^2+y -5/4 and ... (HOMC 2013 Q14)
Source:
August 1, 2019
algebra
system of equations
Problem Statement
Solve the system of equations
{
x
3
+
1
3
y
=
x
2
+
x
−
4
3
y
3
+
1
4
z
=
y
2
+
y
−
5
4
z
3
+
1
5
x
=
z
2
+
z
−
6
5
\begin{cases} x^3+\frac13 y=x^2+x -\frac43 \\ y^3+\frac14 z=y^2+y -\frac54 \\ z^3+\frac15 x=z^2+z -\frac65 \end{cases}
⎩
⎨
⎧
x
3
+
3
1
y
=
x
2
+
x
−
3
4
y
3
+
4
1
z
=
y
2
+
y
−
4
5
z
3
+
5
1
x
=
z
2
+
z
−
5
6
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