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Soros Olympiad in Mathematics
II Soros Olympiad 1995 - 96 (Russia)
9.1
(x-1)(x^2-1) ...(x^{101}-1)>=0 (II Soros Olympiad 1995-96 R3 9.1)
(x-1)(x^2-1) ...(x^{101}-1)>=0 (II Soros Olympiad 1995-96 R3 9.1)
Source:
June 4, 2024
algebra
inequalities
Problem Statement
Solve the inequality
(
x
−
1
)
(
x
2
−
1
)
(
x
3
−
1
)
⋅
.
.
.
⋅
(
x
100
−
1
)
(
x
101
−
1
)
≥
0
(x-1)(x^2-1)(x^3-1)\cdot ...\cdot (x^{100}-1)(x^{101}-1)\ge 0
(
x
−
1
)
(
x
2
−
1
)
(
x
3
−
1
)
⋅
...
⋅
(
x
100
−
1
)
(
x
101
−
1
)
≥
0
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