\(a\) and \(b\) are real numbers such that

\[a^4+a^2b^2+b^4=900\]

\[a^2+ab+b^2=45\]

What is the value of \(2ab\)?

This problem is from the OMO-2012.

This problem is from the set "Olympiads and Contests Around the World -1". You can see the rest of the problems here.

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