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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
9.6
radicals simplify -- VI Soros Olympiad 1999-00 Round 1 9.6
radicals simplify -- VI Soros Olympiad 1999-00 Round 1 9.6
Source:
May 21, 2024
algebra
Problem Statement
For all valid values of
a
a
a
and
b
b
b
, simplify the expression
4
b
−
a
2
+
2
a
b
+
4
+
a
4
a
b
−
10
b
2
−
8
+
b
.
\frac{\sqrt{4b-a^2+2ab+4}+a}{\sqrt{4ab-10b^2-8}+b}.
4
ab
−
10
b
2
−
8
+
b
4
b
−
a
2
+
2
ab
+
4
+
a
.
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