`x^2-2x+3m-1=0`

Theo hệ thức Viète

`{(x_1+x_2=-b/a=2),(x_1x_2=c/a=3m-1):}`

Theo đề bài

`x_1^2+x_2^2`

`= (x_1+x_2)^2-2x_1x_2`

`= 2^2-2(3m-1)`

`= 4-6m+2`

`= 6-6m`.

`b)`

`sqrt[x_1]+sqrt[x_2] (x_1; x_2>=0)`

Đặt `A=sqrt[x_1]+sqrt[x_2] (A>=0)`

`A^2=(sqrt[x_1]+sqrt[x_2])^2`

`A^2=x_1+2sqrt[x_1x_2]+x_2`

`A^2=2+2sqrt[3m-1]`

`A=sqrt[2+2sqrt[3m-1]]`