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: Define the integers and form the equation. Let the first even integer be x. Since the integers are consecutive even integers, the next even integer is x+2. The sum of the squares of these two integers is 244. x^2 + (x+2)^2 = 244 Step 2: Expand and simplify the equation to form a quadratic equation. x^2 + (x^2 + 4x + 4) = 244 2x^2 + 4x + 4 = 244 Subtract 244 from both sides: 2x^2 + 4x + 4 - 244 = 0 2x^2 + 4x - 240 = 0 Divide the entire equation by 2 to simplify: x^2 + 2x - 120 = 0 The quadratic equation is x^2 + 2x - 120 = 0. Step 3: Solve the quadratic equation for x. We can factor the quadratic equation x^2 + 2x - 120 = 0. We need two numbers that multiply to -120 and add to 2. These numbers are 12 and -10. (x+12)(x-10) = 0 This gives two possible values for x: x+12 = 0 x = -12 x-10 = 0 x = 10 Step 4: Find the pairs of consecutive even integers. Case 1: If x = 10 The first integer is 10. The second integer is x+2 = 10+2 = 12. Check: 10^2 + 12^2 = 100 + 144 = 244. Case 2: If x = -12 The first integer is -12. The second integer is x+2 = -12+2 = -10. Check: (-12)^2 + (-10)^2 = 144 + 100 = 244. The integers are either 10 and 12 or -12 and -10. Send me the next one 📸