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: Write down the given equations. We are given: x^2 + y^2 = 10 xy = 3 Step 2: Use the algebraic identity for (x+y)^2. The identity is: (x+y)^2 = x^2 + 2xy + y^2 Rearrange the terms to group x^2 + y^2: (x+y)^2 = (x^2 + y^2) + 2xy Step 3: Substitute the given values into the identity. Substitute x^2 + y^2 = 10 and xy = 3 into the rearranged identity: (x+y)^2 = (10) + 2(3) Step 4: Simplify the expression. (x+y)^2 = 10 + 6 (x+y)^2 = 16 Step 5: Solve for x+y by taking the square root of both sides. x+y = ±sqrt(16) x+y = ± 4 The value of x+y is ± 4.