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Home » Closed Syllable Words: The Secret Rule Every Teacher Should Teach! - Carbonext

Closed Syllable Words: The Secret Rule Every Teacher Should Teach! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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So, number of 8-digit numbers **without** consecutive 3s is 55.
Thus, the number **with** at least one pair of consecutive 3s is:
- 55 = \boxed{201}
\frac{a + 2b}{a - 2b} + \frac{a - 2b}{a + 2b} = 2.
Find the value of $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $.
Let’s simplify the left-hand side. Let $ x = \frac{a + 2b}{a - 2b} $....
x + \frac{1}{x} = 2 \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2...
\frac{a + 2b}{a - 2b} = 1.
Cross-multiplying:
a + 2b = a - 2b \Rightarrow 2b = -2b \Rightarrow 4b = 0 \Rightarrow b...

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