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
To make the expression x^2 + (8x)/(3) a perfect square, we need to add a constant term. A perfect square trinomial has the form (x+b)^2 = x^2 + 2bx + b^2. Step 1: Identify the coefficient of the x term in the given expression. The expression is x^2 + (8)/(3)x. Comparing this to x^2 + 2bx, we have 2b = (8)/(3). Step 2: Solve for b. 2b = (8)/(3) Divide both sides by 2: b = (8)/(3 × 2) b = (8)/(6) Simplify the fraction: b = (4)/(3) Step 3: Calculate the constant term b^2 that completes the square. The term to be added is b^2. b^2 = ((4)/(3))^2 b^2 = (4^2)/(3^2) b^2 = (16)/(9) Step 4: Match the result with the given options. The value (16)/(9) corresponds to option C. The final answer is C. (16)/(9). Send me the next one 📸