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1985 All Soviet Union Mathematical Olympiad
414
ASU 414 All Soviet Union MO 1985 x/(2+(x+(2+(x+(2+..))))=1
ASU 414 All Soviet Union MO 1985 x/(2+(x+(2+(x+(2+..))))=1
Source:
August 5, 2019
algebra
equation
recurrence relation
Problem Statement
Solve the equation ("
2
2
2
" encounters
1985
1985
1985
times):
x
2
+
x
2
+
x
2
+
.
.
.
x
2
+
1
+
x
=
1
\dfrac{x}{2+ \dfrac{x}{2+\dfrac{x}{2+... \dfrac{x}{2+\sqrt {1+x}}}}}=1
2
+
2
+
2
+
...
2
+
1
+
x
x
x
x
x
=
1
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