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Grigore Moisil Intercounty
2005 Grigore Moisil Urziceni
1
System of four variables
System of four variables
Source:
November 28, 2019
equations
system of equations
algebra
Problem Statement
Find the nonnegative real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
that satisfy the following system:
{
a
3
+
2
a
b
c
+
b
c
d
−
6
=
a
a
2
b
+
b
2
c
+
a
b
d
+
b
d
2
=
b
a
2
b
+
a
2
c
+
b
c
2
+
c
d
2
=
c
d
3
+
a
b
2
+
a
b
c
+
b
c
d
−
6
=
d
\left\{ \begin{matrix} a^3+2abc+bcd-6&=&a \\a^2b+b^2c+abd+bd^2&=&b\\a^2b+a^2c+bc^2+cd^2&=&c\\d^3+ab^2+abc+bcd-6&=&d \end{matrix} \right.
⎩
⎨
⎧
a
3
+
2
ab
c
+
b
c
d
−
6
a
2
b
+
b
2
c
+
ab
d
+
b
d
2
a
2
b
+
a
2
c
+
b
c
2
+
c
d
2
d
3
+
a
b
2
+
ab
c
+
b
c
d
−
6
=
=
=
=
a
b
c
d
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