2(a + b) = (3 + \sqrt5)(a - b) - DNSFLEX
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:
📰 This Burning Chilli Shocked the World—Here’s Why It Feels Like hell 📰 The Deadliest Spice on Earth: One Bite Gets Under the Skin 📰 Start Eating This Burning Chilli—You’ll Feel Every Flame Before the Pain 📰 Simplifying 8W 48 📰 Since Abc 1 We Can Assume A Racxy B Racyz C Raczx And By Am Gm 📰 Since Racxz Racxy Cdot Racyz Ac Rac1B And Similarly Raczx Rac1C But Racxz Raczx B Rac1B 📰 Since Activity Units Of Enzyme Activity After 15 Hours Is 25600 📰 Since Paint Is Usually Sold In Whole Liters Round Up To 1 Liter 📰 Sip And Smile The Ultimate Guide To Good Morning Coffee That Wakes You Up 📰 Sip This Powerhouse Tea Ginger Root Could Cure Your Scofflaw And More 📰 Sizzling Garlic Butter Steak Bites Thatll Make You Hungry Every Time 📰 Slay Every Occasion With These Stunning Rose Gold Gold Dressesgolden Perfection 📰 Sleep Like A Champion 5 Must Use Good Night Blessings That Work Every Time 📰 Slender Stylish And Clear The Glass Desk You Need To See 📰 Smart Loyal Athleticgerman Shepherd Mixed With Labrador Meet The Ultimate Family Dog 📰 Snack Smart Snack Gluten Free Why This Popcorn Is A Must Try 📰 Snap The Perfect Good Afternoon Snapeyes Will Selfie In Instant Joy 📰 Snapchats 1 Breakout Ga Feature Youre Overlooking Watch Views SoarFinal 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
