|a-b|=√(a-b)^2=√(a^2-2ab+b^2)
=√(|a|^2-2ab+|b|^2)
=√6
∴|a|^2-2ab+|b|^2=6
|a|^2+|b|^2=6+2ab
=6+2x1
=8
|a|^2+2ab+|b|^2=8+2ab=8+2x1=10
∴√(a+b)^2=|a+b|=√10
|a-b|=√(a-b)^2=√(a^2-2ab+b^2)
=√(|a|^2-2ab+|b|^2)
=√6
∴|a|^2-2ab+|b|^2=6
|a|^2+|b|^2=6+2ab
=6+2x1
=8
|a|^2+2ab+|b|^2=8+2ab=8+2x1=10
∴√(a+b)^2=|a+b|=√10