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Home » The number of ways to choose 2 signatures from 5 is: - Londonproperty

The number of ways to choose 2 signatures from 5 is: - Londonproperty

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 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.

📌 Discriminant: $ 42^2 - 4\cdot14\cdot27 = 1764 - 1512 = 252 = 36 \cdot 7 $.

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