解方程(x2+1)(y2+1)=10、(x+y)(xy-1)=3

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 06:57:24

解方程(x2+1)*(y2+1)=10、(x+y)*(xy-1)=3
解方程(x2+1)*(y2+1)=10、(x+y)*(xy-1)=3

解方程(x2+1)*(y2+1)=10、(x+y)*(xy-1)=3
(x²+1)(y²+1)=10
x²y²+x²+y²+1=10
x²y²-2xy+1+x²+y²+2xy=10
(xy-1)²+(x+y)²=10
[(xy-1)+(x+y)]²-2(x+y)(xy-1)=10
(x+y)(xy-1)=3代入
[(xy-1)+(x+y)]²=16
(xy-1)+(x+y)=4或(xy-1)+(x+y)=-4
x+y和xy-1是方程t²-4t+3=0或t²+4t+3=0的根.
t²-4t+3=0 (t-1)(t-3)=0 t=1或t=3
x+y=1 xy-1=3 xy=4 x,y是方程m²-m+4=0的根,方程无实根.
x+y=3 xy-1=1 xy=2 x,y是方程m²-3m+2=0的根.
(m-1)(m-2)=0 m=1或m=2
x=1 y=2或x=2 y=1
t²+4t+3=0 (t+1)(t+3)=0 t=-1或t=-3
x+y=-1 xy-1=-3 xy=-2 x,y是方程m²+m-2=0的根,
(m-2)(m+1)=0 m=2或m=-1
x=2 y=-1或x=-1 y=2
x+y=-3 xy-1=-1 xy=0 x,y是方程m²+3m=0的根.
m(m+3)=0 m=0或m=-3
x=0 y=-3或x=-3 y=0
综上,得：
x=1 y=2
x=2 y=1
x=2 y=-1
x=-1 y=2
x=0 y=-3
x=-3 y=0

解方程(x2+y2)2+1=x2+y2+2xy 一元二次解方程 (5 19:28:28)已知（x2+y2) (x2-1+y2)=12试求出x2+y2的值解方程(x2+1)*(y2+1)=10、(x+y)*(xy-1)=3 x2+y2=1和x2+y2-4x+2y=4解这组方程, 方程(x2+y2-2)(x2+y2+1)=0表示的图形是___________2代表平方方程x(x2+y2-1)=0和方程x2+(x2+y2-1)=0它们表示的图形双曲线x2-y2/4=1的渐近线方程 x2-y2=1图像急救、进来,解方程：y=x+1 ① { x2-y2=5② 方程x+y=x2-xy+y2+1的实数解为? 1、方程x2-y2=105的正整数解有________组. 与圆x2+y2-4x+2y+4=0关于直线x-y+3=0成轴对称的圆的方程A.X2+Y2-8X+10Y+40=OB.X2+Y2-8X+1OY+20=0C.X2+Y2+8X-10Y+40=0D.X2+Y2+8X-10Y+20=0 (x2+y2)(x2+y2+1)=20求x2+y2的值迅速啊``````````````作业啊````` 解方程组 x2 -2xy -y2 =1 2x2 -5xy -3y2 =0 解方程组 x2+2xy+y2-4=0 x2-2xy+y2-1=0 解方程组：｛x2+y2=13,x2-2xy+y2=1要完整过程！！！~~ 解方程组｛3x2-y2=8 {4x2+12xy+9y2=1 {x2+2xy+y2-4=0 x2+xy+y2=4 4x2-9y2=0 x2-2xy+y2-1=0还有{x2+y2=4xy-y2+4=0x2-----x的平方 y2------y的平方还有{2x-3y=12x2-3xy+y2-4x+3y-3=0 matlab如何将一组数代入原方程的字母里?syms x1 x2 x3 x4 y1 y2 y3 y4 X1 X2 X3 X4 Y1 Y2 Y3 Y4A=[x1,y1,1,0,0,0,-x1*X1,-y1*X1;0,0,0,x1,y1,1,-x1*Y1,-y1*Y1;x2,y2,1,0,0,0,...-x2*X2,-y2*X2;0,0,0,x2,y2,1,-x2*Y2,-y2*Y2;x3,y3,1,0,0,0,-x3*X3,-y3*X3;