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Solve sqrt(x+1)+sqrt(x+3) = sqrt(2x-1)+sqrt(2x+1)

Source:

May 22, 2008
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Problem Statement

Find all real numbers x x such that \sqrt{x\plus{}1}\plus{}\sqrt{x\plus{}3} \equal{} \sqrt{2x\minus{}1}\plus{}\sqrt{2x\plus{}1}.
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