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Home » Now, subtract the number of arrangements where the two N's are adjacent. - DNSFLEX

Now, subtract the number of arrangements where the two N's are adjacent. - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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r = \frac{1 + \frac{1}{2} \cdot \frac{2\sqrt{7}}{3}}{1 - \frac{3}{2} \...
As before, this evaluates to $ -\frac{5 + 2\sqrt{7}}{9} $, but this is...
Alternatively, let the first term be $ A $, common difference $ d $, s...
A^2 + (A+3d)^2 = A^2 + A^2 + 6Ad + 9d^2 = 2A^2 + 6Ad + 9d^2.
Sum of all terms: $ 4A + 6d $, square: $ 16A^2 + 48Ad + 36d^2 $.
Set equal:
2A^2 + 6Ad + 9d^2 = 16A^2 + 48Ad + 36d^2
\Rightarrow 0 = 14A^2 + 42Ad + 27d^2.
Divide by $ d^2 $: let $ x = \frac{A}{d} $, then:
14x^2 + 42x + 27 = 0.

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