2(a + b) = (3 + \sqrt5)(a - b) - ToelettAPP
Mastering the Equation: Solving 2(a + b) = (3 + √5)(a - b)
Mastering the Equation: Solving 2(a + b) = (3 + √5)(a - b)
Understanding algebraic equations is a fundamental skill in mathematics, and equations involving radicals like √5 often appear in advanced algebra, trigonometry, and mathematical modeling. One such equation that learners frequently encounter is:
> 2(a + b) = (3 + √5)(a - b)
Understanding the Context
Whether you’re solving for one variable in terms of the other or exploring deeper algebraic properties, mastering this equation strengthens your problem-solving abilities. In this article, we’ll guide you step-by-step through simplifying, solving, and interpreting the equation — all optimized for clarity and SEO-friendly content.
What Does the Equation Represent?
The equation
2(a + b) = (3 + √5)(a − b)
is a linear relationship linking two expressions involving variables a and b. The term (3 + √5) is an irrational coefficient, making this equation ideal for practicing simplification and algebraic manipulation, especially when working with radicals.
Key Insights
Step-by-Step Solution
Step 1: Expand both sides
Start by expanding both sides to eliminate parentheses:
Left-hand side:
2(a + b) = 2a + 2b
🔗 Related Articles You Might Like:
📰 er to die 📰 eradimaging 📰 eragon cast 📰 Check Out These Chickensbelieve It Or Face The Truth Wow They Were Worth The Click 📰 Check Using The Pythagorean Theorem 72 242 49 576 625 And 252 625 📰 Chicago Map Revealed Uncover The Citys Hidden Gems Hidden Dangers Zone By Zone 📰 Choose 2 Distinct Gaps Out Of 5 📰 Christmas Is Coming See What Madeas Bold New Holiday Collection Revealed 📰 Chronological Marvel Mastery See How Every Movie Built The Epic Universe 📰 Circuit Pulse Driving Beats Paired With Futuristic Lyrical Imagery 📰 Circumference C 2Pi R 314 📰 Clean Sleek And Unforgettable The Marble Side Table Thats Taking Interior Decorations By Storm 📰 Click Download Shinetop Lunch Clipart Thatll Boost Your Brand Instantly 📰 Click Here These Lyrics To Funk You Up Will Make You Dance And Text Endlessly 📰 Click Here To Explore The Stunning Map Of Canada The Usa Hidden Details You Wont Believe 📰 Click To See How Magic Slot Games Are Rewriting Winning Stories 📰 Click To Unlock The Crazy Lyrics To Green Days Brain Stewitll Leave You Speechless 📰 Clickbait Phrasing Was Intentionally Avoided In Favor Of Clarity And Academic Respect While Maintaining Seo Friendly StructureFinal Thoughts
Right-hand side:
(3 + √5)(a − b) = 3a − 3b + a√5 − b√5
So, the equation becomes:
2a + 2b = 3a − 3b + a√5 − b√5
Step 2: Move all terms to one side
Collect every term to the left to group like terms:
2a + 2b − 3a + 3b − a√5 + b√5 = 0
Combine like terms:
- a-terms: 2a − 3a = −a
- b-terms: 2b + 3b = 5b
- radical terms: −a√5 + b√5 = √5(b − a)
Resulting equation:
−a + 5b + √5(b − a) = 0
