若X*X+Y*Y-4X+6Y+13=0,求X-Y 已知1/a-1/b=2求(2a-ab-2b)/(a+ab-b)
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若X*X+Y*Y-4X+6Y+13=0,求X-Y 已知1/a-1/b=2求(2a-ab-2b)/(a+ab-b)
x²+y²-4x+6y+13=0
(x-2)²+(y+3)²=0
所以x-2=0 x=2
y+3=0 y=-3
x-y=2-(-3)=5
1/a-1/b=2
(b-a)/ab=2
a-b+2ab=0
a-b=-2ab
a-b+ab=-ab
2(a-b)-ab=-4ab-ab=-5ab
(2a-ab-2b)/(a+ab-b)=(-5ab)/(-ab)=5
X*X+Y*Y-4X+6Y+13=0
(x-2)²+(Y+3)²=0
x-2=0
x=2
Y+3=0
Y=-3
X-Y=2+3=5
已知1/a-1/b=2求(2a-ab-2b)/(a+ab-b)
分子分母同除以ab得:
(2a-ab-2b)/(a+ab-b)
=(2/b-1-2/a)/(1/b+1-1/a)
=(-4-1)/(-2+1)
=-5/(-1)
=5
X*X+Y*Y-4X+6Y+13=0
(x-2)^2+(y+3)^2=0
x=2 y=-3
,X-Y=2-(-3)=5
1/a-1/b=2
a-b=-2ab
(2a-ab-2b)/(a+ab-b) =(-4ab-ab)/(-2ab+ab)=5
(1)对原式进行配方可得(X-2)^2+(Y+3)^2=0,所以X=2,Y=-3,X-Y=5
(2)根据1/a+1/b=2,可得b-a=2ab
所以所求式的分子=2a-ab-2b=-ab-2(b-a)=-ab-4ab=-5ab (将b-a=2ab代入)
同时,所求式分母=a+ab-b=ab-(b-a)=ab-2ab=-ab
所以所求式=5
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