Sabemos $a + b = 10$ y $a^2 + b^2 = 58$. Para encontrar $ab$, usamos: - High Altitude Science
Solve for $ ab $ Given $ a + b = 10 $ and $ a^2 + b^2 = 58 $
Solve for $ ab $ Given $ a + b = 10 $ and $ a^2 + b^2 = 58 $
Understanding the relationship between sum and squares is key in algebra—especially when solving equations involving two variables. In this article, we explore how to find the product $ ab $ when given $ a + b = 10 $ and $ a^2 + b^2 = 58 $. This seemingly simple problem reveals powerful techniques used in solving quadratic relationships and contributes to real-world applications in physics, engineering, and data analysis.
The Equation Setup
Understanding the Context
We are given:
$$
a + b = 10
$$
$$
a^2 + b^2 = 58
$$
Our goal is to find the value of $ ab $.
Use the Identity for $ (a + b)^2 $
Recall the fundamental algebraic identity:
$$
(a + b)^2 = a^2 + 2ab + b^2
$$
We can rearrange this to solve for $ ab $:
$$
(a + b)^2 = a^2 + b^2 + 2ab
$$
Substitute Known Values
Key Insights
Plug in the given values:
$$
10^2 = 58 + 2ab
$$
$$
100 = 58 + 2ab
$$
Solve for $ 2ab $
Subtract 58 from both sides:
$$
100 - 58 = 2ab
$$
$$
42 = 2ab
$$
Find $ ab $
Divide both sides by 2:
$$
ab = rac{42}{2} = 21
$$
🔗 Related Articles You Might Like:
📰 Black Ops 6 Zombies Exploding in ChILL Chaos — Real-Life Zombie Warfare You Won’t Ignore! 📰 Inside Black Ops 6 Zombies: The Ultimate Nueper Armageddon – Play the Ultimate Survival Zombie Mix! 📰 Black Ops 6 Zombies Revealed: Unleash Hell on Earth with the Scariest Zombie Battle Ever! 📰 The Only Couch Covers Guaranteed To Elevate Your Space Like Never Before 📰 The Only Gem That Unlocks Inner Power Red Jasper Surprises Everyone 📰 The Only Reliable Parts Mechanics Refuse To Trustnow Revealed 📰 The Only Repollo Trick That Actually Works In 2025 📰 The Only Retriever Doodle Mini Thats Taking The Doodle World By Storm 📰 The Only Rugby Shirts Rumored To Turn Heads At Every Scrumstep Up 📰 The Only Rump Roast Thats Tender Juicy And Outrageous 📰 The Only Selvedge Denim Technique That Survivors Still Use Today 📰 The Only Semi Permanent Shade That Feels Permanentsee The Result Immediately 📰 The Only Shoes That Adjust To Your Day Shoe Depots Game Changing Comfort Revealed 📰 The Only Shrimp Tempura Roll Thats Worth Every Second Spent 📰 The Only Wool Rug That Makes Everyone Fall In Love With Your Floor 📰 The Overlooked Scandinavian Practice Changing How The World Dreams At Night 📰 The Pain Lasted Too Longevery Scar A Silent Reminder Of Your Rings Tragic Escape 📰 The Partner You Never Asked For In Your Homes CleanlinessFinal Thoughts
Conclusion
The product of $ a $ and $ b $ is:
$$
oxed{21}
$$
This elegant solution shows how algebraic identities simplify complex problems. Whether you're solving for variables in math contests, deriving formulas in physics, or modeling relationships in data science, understanding how sums and squares connect to products is invaluable. Remember: sometimes, all you need to unlock a mystery is one key identity.
By mastering such techniques, you enhance your problem-solving toolkit and improve your grasp of algebra’s core principles—essential for academic success and practical applications.
Keywords: $ a + b = 10 $, $ a^2 + b^2 = 58 $, find $ ab $, algebraic identity, solve for product, mathematical technique, algebra practice.
