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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
10.2
(\pi-2)/2 + 2/(1+cos (2\sqrtx})+arcsin (VI Soros Olympiad 1990-00 R1 10.2)
(\pi-2)/2 + 2/(1+cos (2\sqrtx})+arcsin (VI Soros Olympiad 1990-00 R1 10.2)
Source:
May 28, 2024
algebra
trigonometry
Problem Statement
Solve the equation
π
−
2
2
+
2
1
+
sin
(
2
x
)
+
a
r
c
c
o
s
(
x
3
−
8
x
−
1
)
=
t
g
2
x
−
x
4
+
x
3
−
5
x
2
−
8
x
−
24
\frac{\pi-2}{2} + \frac{2}{1+\sin (2\sqrt{x})}+arccos(x^3-8x-1)=tg^2\sqrt{x}- \sqrt{x^4+x^3-5x^2-8x-24}
2
π
−
2
+
1
+
sin
(
2
x
)
2
+
a
rccos
(
x
3
−
8
x
−
1
)
=
t
g
2
x
−
x
4
+
x
3
−
5
x
2
−
8
x
−
24
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