Given the set a = {x | x ^ 2-1 = 0}, B = {x | x ^ 2-2ax-b = 0}, if B ≠ an empty set and B is contained in a, find the value of a and B?

Given the set a = {x | x ^ 2-1 = 0}, B = {x | x ^ 2-2ax-b = 0}, if B ≠ an empty set and B is contained in a, find the value of a and B?

A={x|x^2-1=0}={-1,1}
B={x|x^2-2ax-b=0}
If B ≠ an empty set and B is contained in a
Then B = {- 1} or B = {1} or B = {- 1,1}
(1) When B = {- 1}
(-1)+(-1)=2a,(-1)*(-1)=-b
So a = - 1, B = - 1
(2) When B = {1}
1+1=2a,1*1=-b
So a = 1, B = - 1
(3) When B = {- 1,1}
-1+1=2a,-1*1=-b
So a = 0, B = 1
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2aX squared-2ay4 power

=2A (the fourth power of X & # 178; - y)
=2a(x+y²)(x-y²)

The square of 2A (the square of x plus 1) minus the fourth power of 2aX

2a(x²+1)²-2ax^4
=2a[(x²+1)²-x^4]
=2a(x²+1+x²)(x²+1-x²)
=2a(2x²+1)