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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
11.7
x^7+x^2+1=0, x^5-x^4 + x^2- x+1.001=0 (III Soros Olympiad 1996-97 R3 11.7)
x^7+x^2+1=0, x^5-x^4 + x^2- x+1.001=0 (III Soros Olympiad 1996-97 R3 11.7)
Source:
May 31, 2024
algebra
polynomial
Problem Statement
Let us assume that each of the equations
x
7
+
x
2
+
1
=
0
x^7 + x^2 + 1= 0
x
7
+
x
2
+
1
=
0
and
x
5
−
x
4
+
x
2
−
x
+
1.001
=
0
x^5- x^4 + x^2- x + 1.001 = 0
x
5
−
x
4
+
x
2
−
x
+
1.001
=
0
has a single root. Which of these roots is larger?
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