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Soros Olympiad in Mathematics
IV Soros Olympiad 1997 - 98 (Russia)
9.2
nested radicals (IV Soros Olympiad 1997-98 Correspondence 9.2)
nested radicals (IV Soros Olympiad 1997-98 Correspondence 9.2)
Source:
June 1, 2024
algebra
Radicals
Problem Statement
Solve the equation
2
1
+
x
1
+
(
x
+
1
)
1
+
(
x
+
2
)
1
+
(
x
+
3
)
(
x
+
5
)
=
x
2\sqrt{1+x\sqrt{1+(x+1)\sqrt{1+(x+2)\sqrt{1+(x+3)(x+5)}}}}=x
2
1
+
x
1
+
(
x
+
1
)
1
+
(
x
+
2
)
1
+
(
x
+
3
)
(
x
+
5
)
=
x
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