Question

已知集合{1,a+b,a}={0,a/b,b},求实数a,b的值?

PS:上述/为分数线 知道的请无视 还有就是请明细过程 步骤全面 格式清晰 简单易懂 ..谢谢解答..

Answer 1

2中情况：
若a+b=0 则a/b= -1 b=1 a=-1
若a=0 则 a/b= 0 集合中出现相同元素 不成立
所以 b=1 a=-1

Answer 2

{1,a+b,a}={0,a/b,b}
As 0 is not equal to 1, then
case I
if 1=b
then a/b = a/1 = a, so
a+b = 0 => a = -1

a=-1, b=1

case II
1=a/b => a=b ( for b is not equal to 0 )
if 0=a then contradict b is not equal to 0 (rejected)
if 0=a+b => a=-b => a=b=0 then contradict b is not equal to 0 (rejected)

Therefore only case I is valid
a=-1, b=1

Answer 3

易知，a+b=0,且b=1.∴a=-1,b=1.集合{1,a+b,a}={-1,0,1}.集合{0,a/b.b}={-1,0,1}.∴a=-1,b=1符合题设。

Answer 4

a=-1,b=1