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9
SMT 2007 Algebra #9
SMT 2007 Algebra #9
Source:
June 27, 2012
quadratics
Problem Statement
Find
a
2
+
b
2
a^2+b^2
a
2
+
b
2
given that
a
,
b
a, b
a
,
b
are real and satisfy
a
=
b
+
1
a
+
1
b
+
1
a
+
⋯
;
b
=
a
−
1
b
+
1
a
−
1
b
+
⋯
a=b+\frac{1}{a+\frac{1}{b+\frac{1}{a+\cdots}}}; b=a-\frac{1}{b+\frac{1}{a-\frac{1}{b+\cdots}}}
a
=
b
+
a
+
b
+
a
+
⋯
1
1
1
;
b
=
a
−
b
+
a
−
b
+
⋯
1
1
1
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