根号a+根号b=根号3+根号2,根号ab=根号6+根号2,则a+b=

问题描述:

根号a+根号b=根号3+根号2,根号ab=根号6+根号2,则a+b=

√a+√b=√3+√2 (1) √ab=√6+√2 (2) (2)两边平方得:ab=8+4√3 (1)两边平方得:a+b+2√ab=5+2√6 (3) (2) 两边×2得:2√ab=2√6+2√2 (4) (4)-(5)得:a+b=5-2√2 答:a+b=5-2√2 ab=8+4√3