`d){(x+y=5),(x^4+y^4=97):}`

 ta có :`x^4+y^4=97`

`<=>x^4+y^4+2x^2y^2-2x^2y^2=97`

`<=>(x^2+y^2)^2-2x^2y^2=97`

`<=>(x^2+y^2+2xy-2xy)^2-2x^2y^2=97`

`<=>(25-2xy)^2-2x^2y^2=97`

`<=>625-100xy+4x^2y^2-2x^2y^2=97`

`<=>2x^2y^2-100xy+528=0`

`<=>(xy-44)(xy-6)=0`

`<=>[(xy=44),(xy=6):}`

`=>[(x=44/y),(x=6/y):}(yne0)`

Do đó `x+y=5` trở thành :

`[(44/y+y=5),(6/y+y=5):}`

`<=>[(44+y^2=5y),(6+y^2=5y):}`

`<=>[(y^2-2.5y. 1/2+25/4-25/4+44=0),(y^2-5y+6=0):}`

`<=>[((y-5/2)^2=-151/4 (voli)),(y^2-2y-3y+6=0):}`

`<=>(y-2)(y-3)=0`

`<=>[(y=2),(y=3):}`

`=>[(x=22),(x=2):}`

`e){(x^2+xy+y^2=3),(x^4+y^4=17):}`

`x^4+y^4=17`

`<=>(x^2+y^2)^2-2x^2y^2=17`

do `x^2+xy+Y^2=3<=>x^2+y^2=3-xy`

`<=>(3-xy)^2-2x^2y^2=17`

`<=>x^2y^2-2x^2y^2-6xy+9-17=0`

`<=>x^2y^2+6xy+8=0`

`<=>(xy+2)(xy+4)=0`

`<=>[(xy=-2),(xy=-4):}`

`=>[(x=-2/y),(x=-4/y):}(y ne0)`

`x^4+y^4=17` trở thành:

`<=>[(y^4+(-2/y)^4=17),(y^4+(-4/y)^4=17):}`

`=>[(y^8+16=17y^4),(y^8+256=17y^4):}`

`<=>[(y^8-16y^4-y^4+16=0),(y^8-17y^4+ (17/2)^2 +735/4=0(voli)):}`

`<=>(y^4-16)(y^4-1)=0`

`<=>(y^2-4)(y^2-1)(y^2+4)(y^2+1)=0`

do `y^2+4>0;y^2+1>0`

`=>(y^2-4)(y^2-1)=0`

`<=>[(y^2=4),(y^2=1):}`

`<=>[(y=2),(y=-2),(y=1),(y=-1):}`

`=>[(x=-1),(x=1),(x=-2),(x=2):}`