MathDB
Problems
Contests
International Contests
IMO Shortlist
1971 IMO Shortlist
3
Find the value of x^5+y^5+z^5
Find the value of x^5+y^5+z^5
Source:
September 22, 2010
algebra
system of equations
Vieta
Polynomials
IMO Shortlist
Problem Statement
Knowing that the system
x
+
y
+
z
=
3
,
x + y + z = 3,
x
+
y
+
z
=
3
,
x
3
+
y
3
+
z
3
=
15
,
x^3 + y^3 + z^3 = 15,
x
3
+
y
3
+
z
3
=
15
,
x
4
+
y
4
+
z
4
=
35
,
x^4 + y^4 + z^4 = 35,
x
4
+
y
4
+
z
4
=
35
,
has a real solution
x
,
y
,
z
x, y, z
x
,
y
,
z
for which
x
2
+
y
2
+
z
2
<
10
x^2 + y^2 + z^2 < 10
x
2
+
y
2
+
z
2
<
10
, find the value of
x
5
+
y
5
+
z
5
x^5 + y^5 + z^5
x
5
+
y
5
+
z
5
for that solution.
Back to Problems
View on AoPS