請問:兩集合A={(x,y)|3x-2y+3=0}與B={(y+2,x-1)|ax+by+(2a-1)=0},若A=B,則數對(a,b)為???謝謝~~~ 可以麻煩敘述一下是如何解出的嗎?感激!!!?

2016-03-23 3:46 pm

回答 (1)

2016-03-24 1:16 am
✔ 最佳答案
Sol
Set m=y+2,n=x-1
x=n+1,y=m-2
ax+by+(2a-1)
=a(n+1)+b(m-2)+(2a-1)
=bm+an+(3a-2b-1)
B={(y+2,x-1)|ax+by+(2a-1)=0}
={(m,n)|bm+an+(3a-2b-1)=0}
={(x,y)|bx+ay+(3a-2b-1)=0}
So
b/3=a/(-2)=(3a-2b-1)/3=p
b=3p,a=-2p,3a-2b-1=3p
3*(-2p)-2*(3p)-1=3p
-15p=-1
p=-1/15
a=2/15.b=-1/5
(a,b)=(2/15,-1/5)
*****
ax+by+(2a-1)=0
15ax+15bx+30a-15=0
2x-3y-11=0
-2x+3y=11=0
3(y+2)-2(x-1)+3=0


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