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65
Identity with lots of square roots.
Identity with lots of square roots.
Source:
October 4, 2010
algebra
algebraic identities
IMO Shortlist
IMO Longlist
Problem Statement
(
U
S
S
2
)
(USS 2)
(
U
SS
2
)
Prove that for
a
>
b
2
,
a > b^2,
a
>
b
2
,
the identity
a
−
b
a
+
b
a
−
b
a
+
⋯
=
a
−
3
4
b
2
−
1
2
b
{\sqrt{a-b\sqrt{a+b\sqrt{a-b\sqrt{a+\cdots}}}}=\sqrt{a-\frac{3}{4}b^2}-\frac{1}{2}b}
a
−
b
a
+
b
a
−
b
a
+
⋯
=
a
−
4
3
b
2
−
2
1
b
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