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Since \(\sqrt{2}-\sqrt{3} < 0\), then \(|\sqrt{2}-\sqrt{3}| =-(\sqrt{2}-\sqrt{3})\)
\(-\sqrt{2}+\sqrt{3} = m\sqrt{2} + n\sqrt{3}\)
Now, either the question should mention that m and n are integers, then only \(m=-1\) and \(n=1\) work. Hence, m - n = -2
Or, the question is flawed becasue m - n can be any value if m and n are not necessarily integers. For example, m - n = 0 for \(m = \frac{\sqrt{3} -\sqrt{2}}{\sqrt{2} + \sqrt{3}}\) and \(n = \frac{\sqrt{3} -\sqrt{2}}{\sqrt{2} + \sqrt{3}}\)
Not a good question.
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