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Soros Olympiad in Mathematics
IV Soros Olympiad 1997 - 98 (Russia)
9.2
x^2+5\sqrt2 x+a<0 (IV Soros Olympiad 1997-98 R2 9.2)
x^2+5\sqrt2 x+a<0 (IV Soros Olympiad 1997-98 R2 9.2)
Source:
June 1, 2024
algebra
inequalities
parameter
Problem Statement
Find all values of the parameter
a
a
a
for which there exist exactly two integer values of
x
x
x
that satisfy the inequality
x
2
+
5
2
x
+
a
<
0.
x^2+5\sqrt2 x+a<0.
x
2
+
5
2
x
+
a
<
0.
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