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Soros Olympiad in Mathematics
I Soros Olympiad 1994-95 (Rus + Ukr)
10.8
\sqrt{7+8x-16x^2}>=2^{cos^2\pi x}+.. (I Soros Olympiad 1994-95 R2 10.8)
\sqrt{7+8x-16x^2}>=2^{cos^2\pi x}+.. (I Soros Olympiad 1994-95 R2 10.8)
Source:
May 25, 2024
algebra
inequalities
trigonometry
Problem Statement
Find all
x
x
x
for which the inequality holds
7
+
8
x
−
16
x
2
≥
2
cos
2
π
x
+
2
sin
2
π
x
\sqrt{7+8x-16x^2} \ge 2^{\cos^2 \pi x}+2^{\sin ^2 \pi x}
7
+
8
x
−
16
x
2
≥
2
c
o
s
2
π
x
+
2
s
i
n
2
π
x
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