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
Fresh day segunolude0375, let's solve. To show that (sqrt(5) + sqrt(13))^2 > 34, we will expand the left side of the inequality. Step 1: Expand the expression (sqrt(5) + sqrt(13))^2 using the formula (a+b)^2 = a^2 + 2ab + b^2. Here, a = sqrt(5) and b = sqrt(13). (sqrt(5) + sqrt(13))^2 = (sqrt(5))^2 + 2(sqrt(5))(sqrt(13)) + (sqrt(13))^2 Step 2: Simplify the terms. (sqrt(5))^2 = 5 (sqrt(13))^2 = 13 2(sqrt(5))(sqrt(13)) = 2sqrt(5 × 13) = 2sqrt(65) Step 3: Substitute the simplified terms back into the expanded expression. (sqrt(5) + sqrt(13))^2 = 5 + 2sqrt(65) + 13 (sqrt(5) + sqrt(13))^2 = 18 + 2sqrt(65) Step 4: Now we need to show that 18 + 2sqrt(65) > 34. Subtract 18 from both sides of the inequality: 2sqrt(65) > 34 - 18 2sqrt(65) > 16 Step 5: Divide both sides by 2. sqrt(65) > (16)/(2) sqrt(65) > 8 Step 6: Square both sides of the inequality to remove the square root. Since both sides are positive, the inequality direction remains the same. (sqrt(65))^2 > 8^2 65 > 64 Step 7: Conclude the proof. Since 65 > 64 is a true statement, the original inequality (sqrt(5) + sqrt(13))^2 > 34 is also true. We have shown that (sqrt(5) + sqrt(13))^2 > 34. Proven Send me the next one 📸