解方程组x^2-y^2=1&x^2+2y^2=10

2y²+xy=y(2y+x)=0
所以y=0或x=-2y
y=0
x²-y²=x²=12
x=±2√3
x=-2y
x²-y²=3y²=12
y=±2
所以
x=-2√3,y=0
x=2√3,y=0
x=4,y=-2
x=-4,y=2

x^2-y^2=5(x+y)
===> (x+y)(x-y)-5(x+y)=0
===> (x+y)(x-y-5)=0
===> x=-y,或者x=y+5
①当x=-y时,带入第二个有：x^2-x^2+x^2=43
===> x^2=43
===> x=±√43
则,y=±√43
②当x=y+5时,带入第二个有：(y+5)^2+(y+5)*y+y^2=43
===> y^2+10y+25+y^2+5y+y^2=43
===> 3y^2+15y-18=0
===> y^2+5y-6=0
===> (y-1)(y+6)=0
===> y=1,或者y=-6
所以,x=6,或者x=-1
综上：
①x=√43,y=-√43
②x=-√43,y=√43
③x=6,y=-1
④x=-6,y=1

(x+y)(x-y)-(x+y)=0
(x+y)(x-y-1)=0
若x-y-1=0
y=x-1
则4x^2-x^2+2x-1+2x-x+1=0
3x^2-3x=0
3x(x-1)=0
x=0,x=1
y=x-1
若x+y=0
y=-x
则4x^2-x^2+2x+x=0
3x^2+3x=3x(x+1)=0
x=0,x=-1
y=-x
所以
x=0,y=-1
x=1,y=0
x=0,y=0
x=-1,y=1

x^2-(9/4)y^2=0
x^2=(9/4)y^2
y=2x/3或y=-2x/3
y=2x/3
(4/3) x^2+4xy+3y^2=1/3
4/3*x^2+8/3*x^2+4/3*x^2=1/3
16/3*x^2=1/3
x^2=1/16
x=±4
y=2x/3
y=-2x/3
(4/3) x^2+4xy+3y^2=1/3
4/3*x^2-8/3*x^2+4/3*x^2=1/3
0=1/3
不成立
所以
x=4,y=8/3
x=-4,y=-8/3