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National and Regional Contests
Canada Contests
Canada National Olympiad
2022 Canada National Olympiad
1
symmetric algebra
symmetric algebra
Source: 2022 CMO
March 12, 2022
algebra
CMO
inequalities
Problem Statement
If
a
b
+
a
b
+
1
+
a
2
+
b
a
+
b
2
=
0
ab+\sqrt{ab+1}+\sqrt{a^2+b}\sqrt{a+b^2}=0
ab
+
ab
+
1
+
a
2
+
b
a
+
b
2
=
0
, find the value of
b
a
2
+
b
+
a
b
2
+
a
b\sqrt{a^2+b}+a\sqrt{b^2+a}
b
a
2
+
b
+
a
b
2
+
a
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