Đáp án+Giải thích các bước giải:
Đặt `A=sqrt{1+sqrt3+1}+sqrt{1-sqrt3+1}`
`=sqrt{2+sqrt3}+sqrt{2-sqrt3}`
`=>Asqrt2=sqrt2.(sqrt{2+sqrt3}+sqrt{2-sqrt3})`
`Asqrt2=sqrt{4+2sqrt3}+sqrt{4-2sqrt3}`
`Asqrt2=sqrt{3+2sqrt3+1}+sqrt{3-2sqrt3+1}`
`Asqrt2=sqrt{(sqrt3+1)^2}+sqrt{(sqrt3-1)^2}`
`Asqrt2=|sqrt3+1|+|sqrt3-1|`
`Asqrt2=sqrt3+1+sqrt3-1`
`Asqrt2=2sqrt3`
`=>A=(2sqrt3)/sqrt2`
`=sqrt6`
Vậy `sqrt{1+sqrt3+1}+sqrt{1-sqrt3+1}=sqrt6`
