Question

A+B=AXB=A÷B What are the values

of A & B?​

Answer 1

A = 1/2  and B = - 1  ,  A + B = A × B = A ÷ B =  -1/2  if A + B = A × B = A ÷ B

Given:

A + B = A × B = A ÷ B

To Find;

Values of A and B

Solution:

Assume that

A + B = A × B = A ÷ B = k

Hence

A= BK

Substituting

BK + B = BK × B  = Bk  ÷ k

=> B (k + 1)  = B²k   =  k

B²k   =  k

=> B² = 1

=> B = ± 1

B (k + 1)  = B²k  

=> k + 1 = Bk

using B = 1

=> k + 1 = k  => 0 = 1 not possible

using B = - 1

=> k + 1  = - k

=> 2k = -1

=>  k = -1/2

B = -1  , k =  -1/2  ,

A = Bk = -1(-1/2) =1/2

A = 1/2

B = - 1

Verification

A + B = 1/2 - 1 = -1/2

A × B = (1/2)(-1) = -1/2

A ÷ B (1/2) ÷ (-1) = - 1/2

Hence A = 1/2  and B = - 1

A + B = A × B = A ÷ B = -1/2