解二元二次方程组 x^2-xy=6,xy+y^2=4此题原题是英文:Find all ordered pairs (x,y) that satisfy both x^2-xy=6 and xy+y^2=4.
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解二元二次方程组 x^2-xy=6,xy+y^2=4此题原题是英文:Find all ordered pairs (x,y) that satisfy both x^2-xy=6 and xy+y^2=4.
解二元二次方程组 x^2-xy=6,xy+y^2=4
此题原题是英文:
Find all ordered pairs (x,y) that satisfy both x^2-xy=6 and xy+y^2=4.
解二元二次方程组 x^2-xy=6,xy+y^2=4此题原题是英文:Find all ordered pairs (x,y) that satisfy both x^2-xy=6 and xy+y^2=4.
消去常数项:
1式*2-2式*3:2x²-2xy-3xy-3y²=0
即2x²-5xy-3y²=0
(2x+y)(x-3y)=0
得x=-y/2,或x=3y
将x=-y/2代入方程2:-y²/2+y²=4,得:y²=8,得y=2√2,-2√2
将x=3y代入方程2:3y²+y²=4,得y²=1,得:y=1,-1
因此共有4组(-√2,2√2),(√2,-2√2),(3,1),(-3,-1)
x(x-y)=6
x(x+y)=4
两式相除
(x+y)/(x-y)=6/4
x+y=1.5(x-y)
x+y=1.5x-1.5y
0.5x=2.5y
x=5y
(5y)²-5y*y=6
25y²-5y²=6
y²=3/10
y=±(√30)/10
x...
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x(x-y)=6
x(x+y)=4
两式相除
(x+y)/(x-y)=6/4
x+y=1.5(x-y)
x+y=1.5x-1.5y
0.5x=2.5y
x=5y
(5y)²-5y*y=6
25y²-5y²=6
y²=3/10
y=±(√30)/10
x=±(√30)/2
请好评
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