∵a+√c=b+√d∴a-b=√d-√c∵√c，√d是无理数∴当√d=√c√d-√c=0为有理数当√d≠√c时√d-√c为无理数而a-b是有理数∴a-b=√d-√c=0∴a=b，√d=√c∴a=b，d=c
