Question: The sum of two numbers is 15, and their product is 50. What is the sum of their squares?

Thu, 30 Apr 2026 07:55:49 +0000

**The sum of two numbers is 15, and their product is 50. What is the sum of their squares?** A quiet but intriguing math puzzle is sparking thoughtful conversations across mobile devices in the U.S. — especially among users curious about logic, numbers, and patterns behind everyday questions. Now, tackle this: The sum of two numbers is 15, and their product is 50. What is the sum of their squares? This blend of arithmetic logic and real-world relevance makes people ask: *How do numbers connect uniquely?* Understanding the answer reveals more than basic algebra — it builds problem-solving insight with everyday clarity. To solve this, start with two numbers, let’s call them *x* and *y*. We know:
**x + y = 15**
**x × y = 50** Rather than searching wildly, recognize this as a signal from quadratic relationships — a classical setup where sum and product fix a pair uniquely. Use the identity: *x² + y² = (x + y)² – 2xy*. Plugging in the known sum and product:
x² + y² = 15² – 2×50 = 225 – 100 = 125