Solve this multiple-choice question and choose the correct option.

Problem restatementLet the numbers be a and b with ab = 120 and a2 + b2 = 289. Find a + b. Concept/ApproachUse the identity (a + b)2 = a2 + b2 + 2ab. Step-by-step calculation (a + b)2 = 289 + 2×120 = 289 + 240 = 529 a + b = √529 = 23 Verification/Alternative529 is 232. The sum could be −23 algebraically, but the context typically takes the positive sum. Final Answer23

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The product of two numbers is 120 and the sum of their squares is 289. What is the sum of the numbers?

Difficulty: Easy

Correct Answer: 23

Explanation:

Problem restatementLet the numbers be a and b with ab = 120 and a² + b² = 289. Find a + b.

Concept/ApproachUse the identity (a + b)² = a² + b² + 2ab.

Step-by-step calculation (a + b)² = 289 + 2×120 = 289 + 240 = 529 a + b = √529 = 23

Verification/Alternative529 is 23². The sum could be −23 algebraically, but the context typically takes the positive sum.

Final Answer23

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