`1) {(\sqrt{3x+1}+2y=4),(3\sqrt{3x+1}-y=5):}`

Đặt `\sqrt{3x+1}=a(a>=0)`

Hpt `<=> {(a+2y=4),(3a-y=5):}`

`<=> {(a+2y=4),(6a-2y=10):}`

`<=> {(7a=14),(a+2y=4):}`

`<=> {(a=2(tm)),(2+2y=4):}`

`<=> {(a=2),(y=1):}`

Mà `a=\sqrt{3x+1}`

`=> \sqrt{3x+1}=2(đk: x>=-1/3)`

`<=> 3x+1=4`

`<=> 3x=3`

`<=> x=1(tm)`

Vậy `(x,y)=(1,1)`

`2)` `PTHĐGĐ: x^2=(m-2)x+5`

`<=> x^2-(m-2)x-5=0`

`\Delta=(m-2)^2-4.1.(-5)=(m-2)^2+20>0 AAm`

Vậy `(d)` luôn cắt `(P)` tại `2` điểm pb

`b)` Theo HT vi-ét:

`{(x_1+x_2=m-2),(x_1x_2=-5):}`

Mà `x_1+5x_2=0`

Ta có hpt:

`{(x_1+x_2=m-2),(x_1+5x_2=0):}`

`<=> {(4x_2=-m+2),(x_1+x_2=m-2):}`

`<=> {(x_2=(-m+2)/4),(x_1+(-m+2)/4=m-2):}`

`<=> {(x_2=(-m+2)/4),(x_1=(5m-10)/4):}`

Mà `x_1x_2=-5=> (-m+2)/4 . (5m-10)/4 =-5`

`(-m+2)(5m-10)=-80`

`<=> (m-2)^2=16`

`<=> m-2=4` hoặc `m-2=-4`

`<=> m=6` hoặc `m=-2`

Vậy `m=6` hoặc `m=-2` là gtct