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Regional Mathematical Olympiad
2008 India Regional Mathematical Olympiad
2
A system of equations
A system of equations
Source: An Excursion in Mathematics
June 25, 2020
system of equations
equation
algebra
Problem Statement
Solve the system of equation
x
+
y
+
z
=
2
;
x+y+z=2;
x
+
y
+
z
=
2
;
(
x
+
y
)
(
y
+
z
)
+
(
y
+
z
)
(
z
+
x
)
+
(
z
+
x
)
(
x
+
y
)
=
1
;
(x+y)(y+z)+(y+z)(z+x)+(z+x)(x+y)=1;
(
x
+
y
)
(
y
+
z
)
+
(
y
+
z
)
(
z
+
x
)
+
(
z
+
x
)
(
x
+
y
)
=
1
;
x
2
(
y
+
z
)
+
y
2
(
z
+
x
)
+
z
2
(
x
+
y
)
=
ā
6.
x^2(y+z)+y^2(z+x)+z^2(x+y)=-6.
x
2
(
y
+
z
)
+
y
2
(
z
+
x
)
+
z
2
(
x
+
y
)
=
ā
6.
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