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: Use the algebraic identity for (a+b)^2. We know that (a+b)^2 = a^2 + b^2 + 2ab. Step 2: Substitute the given values into the identity. We are given a+b=9 and a^2+b^2=71. (9)^2 = 71 + 2ab 81 = 71 + 2ab Step 3: Solve for ab. Subtract 71 from both sides: 81 - 71 = 2ab 10 = 2ab Divide by 2: ab = (10)/(2) ab = 5 Step 4: Calculate the value of (ab)^3. Substitute the value of ab into (ab)^3: (ab)^3 = (5)^3 (ab)^3 = 5 × 5 × 5 (ab)^3 = 125 The value of (ab)^3 is 125. Send me the next one 📸