Lời giải:

`b)`

`x^2-(2m-1)x-m=0`

`Delta=b^2-4ac=[-(2m-1)]^2-4*1(-m)`

`= 4m^2-4m+1+4m`

`= 4m^2+1>0`

`->` Phương trình luôn có hai no phân biệt

Viet:

`{(x_1+x_2=2m-1),(x_1x_2=-m):}`

Đề:

`[x_1^2+x_2^2-7x_1x_2]/[sqrt[x_1x_2]-1]=1+sqrt[x_1x_2] (m<=0)`

`<=> [(x_1+x_2)^2-2x_1x_2-7x_1x_2]/[sqrt[x_1x_2]-1]=1+sqrt[x_1x_2]`

`<=> [(x_1+x_2)^2-9x_1x_2]/[sqrt[x_1x_2]-1]=1+sqrt[x_1x_2]`

`<=> [(2m-1)^2-9(-m)]/[sqrt[-m]-1]=1+sqrt[-m]`

`<=> [4m^2-4m+1+9m]/[sqrt[-m]-1]=1+sqrt[-m]`

`<=> 4m^2+5m+1=(1+sqrt[-m])(sqrt[-m]-1)`

`<=> 4m^2+5m+1=-m-1`

`<=> 4m^2+6m+2=0`

`<=> (m+1)(2m+1)=0`

`<=> m=-1` (nhận) hoặc `m=-1/2` (nhận)

Vậy `m in {-1;-1/2}`