根号a+根号b=3 (1)
根号a-根号b=3k (2)
(1)+(2) 2√a=3+3k √a=3(1+k)/2
(1)-(2) 2√b=3-3k √b=3(1-k)/2
∵√a≥0 √b≥0
∴3(1+k)/2≥0 k≥-1
3(1-k)/2≥0 k≤1
∴k的取值范围为[-1,1]