Question

A+B=A×B=A÷B find the value of a and b

Answer 1

Answer:

The 3 solutions for (A,B) are (0,0), (½,1) and (½,-1).

Step-by-step explanation:

From A×B = A÷B it follows that A × (B² - 1) = 0

So A = 0 and/or B = ±1 (on account of B² - 1 = 0).  

Case 1) For A=0, A+B = A×B = A÷B is the same as 0+B = 0×B = 0÷B, which after simplification amounts to B=0.

Case 2) For B=1, A+B = A×B = A÷B is the same as A+1 = A×1 = A÷1, which after simplification amounts to A=½.

Case 3) For B=-1, A+B = A×B = A÷B is the same as A+-1 = A×-1 = A÷-1, which after simplification amounts to A=½.