Question

高一数学...

集合A={a,a方,ab} B={1,a,b,}且A=B 求a..b (a b属于R） 值

Answer 1

先行判断一下，很明显集合A中的a与集合B中的1不能对应，否者，两集合有相同的元素1，此情况排除。

如果a^2=a,则有a=-1，a=1舍去。
此时集合A={-1,1,-b}；集合B={1,-1,b},所以有b=0。

Answer 2

A=B
∴a²=1，ab=b或a²=b，ab=1

当a²=1，ab=b时
∴a=1,b为任意实数，或a=-1,b=0
a=1时不满足集合元素的互异性，∴舍去
当a=-1,b=0时
A={-1,1,0}
B={1,-1,0}
A=B成立

当a²=b，ab=1时
a=1,b=1
不满足集合元素的互异性，∴舍去

综上可知，a=-1,b=0

Answer 3

A={a,a^2,ab} B={1,a,b,},A=B
则 a^2=1 或者 ab=1
若a^2=1 ，则a=-1(由集合的互异性,a不能等于1），b=ab=-b,b=0
若ab=1,则a^2=b,ab=a*a^2=a^3=1,a=1,与集合互异性矛盾
故a=-1，b=0

Answer 4

Solution:

∵A = B,
∴ All elements of Set A are same as all elements of Set B.

Case 1:
a² = 1, a = ±1
ab = b, a = +1, no general way to determine the value of b.
ab = b, a = -1, also no general way to determine the value of b.
So, possible sulotion is a = 1 and b = 0, or a = -1 and b = 0

Case 2:
a² = ab, a = b
ab = 1, a²= 1
a = ±1, b = ±1
So, possble solution one is a = b = 1； solution two is a = b = -1.

Because each element of a set is diffenernt from others,
the final solution is a = -1, b = 0.

Answer 5