This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Analyze Option (b) - zero. We are looking for a pair of integers (a,b) such that their sum a+b is zero AND their difference a-b is zero. We set up a system of equations: 1) a+b=0 2) a-b=0 Step 2: Solve the system of equations. Add equation (1) and equation (2): (a+b) + (a-b) = 0+0 2a = 0 a = 0 Substitute a=0 into equation (1): 0+b=0 b=0 Step 3: Verify the solution. The pair of integers is (0,0). For this pair: Sum: a+b = 0+0 = 0 Difference: a-b = 0-0 = 0 Both the sum and the difference are 0. Since 0 is an integer, this pair (0,0) satisfies the condition that both their sum and difference result in zero. Therefore, there is a pair of integers whose sum and difference both result in zero. The final answer is b) zero.