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Algebra Level 4

Find all ordered pairs of real numbers \((a, b)\) such that \({ (x-a) }^{ 2 }+{ (2x-b) }^{ 2 }={ (x-3) }^{ 2 }+{ (2x) }^{ 2 }\) is true for all values of \(x\).

Let \(n\) be the sum of all \(a\)'s in ordered pair \((a, b)\) and \(m\) be the sum of all \(b\)'s in the ordered pair \((a, b)\).

What is \(\frac { n }{ m } \)?

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