若x^2-4y^2=-15,x+2y=3,求x,y的值.

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若x^2-4y^2=-15,x+2y=3,求x,y的值.
若x^2-4y^2=-15,x+2y=3,求x,y的值.

若x^2-4y^2=-15,x+2y=3,求x,y的值.
x²-4y²=-15
(x-2y)(x+2y)=-15
(x-2y)×3=-15
x-2y=-5
x+2y=3
相加得
2x=-2
x=-1
代回得y=2
x=-1,y=2

x^2-4y^2=(x+2y)(x-2y)=-15
x+2y=3
所以x-2y=-15/3=-5
加上x+2y=3
2x=-2
x=-1
代入x+2y=3
-1+2y=3
2y=4
y=2

(X+2y)(x-2y)=-15
x-2y=-15/3=-5
x+2y=3
两式相加除2,x=-1
带入,y=2

x^2-4y^2=(x+2y)(x-2y)=-15
x+2y=3所以x-2y=-5
所以x=-1,y=2

x^2-4y^2=-15 (1)
x+y=3 (2)
由(2)得x=3-y (3)
把(3)代入(1)得
(3-y)^2-4y^2+15=0
9-6y+y^2-4y^2+15=0
-3y^2-6y+24=0
y^2+2y-8=0
(y+4)(y-2)=0
y=-4或y=2
x=7或x=1

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