2(a + b) = (3 + \sqrt5)(a - b) - RoadRUNNER Motorcycle Touring & Travel Magazine

Mastering the Equation: Solving 2(a + b) = (3 + √5)(a - b)

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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.

Solved: Calculate the value of b in the following equality: sqrt(5 ...

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Solved: Calculate the value of b in the following equality: sqrt(5 ...

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Solved: a^5-a^2b^3-a^3b^2+b^5 [Math]

$\sqrt{A^{2}+B^{2}-2 A B \cos \theta}=\sqrt[3]{A^{2}+B^{2}+2 A B \cos \the..$

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

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Final 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

Step 3: Factor intelligent grouping