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Home » Compute the square of \( (3x - 2) \). - Portal da AcÃºstica

Compute the square of \( (3x - 2) \). - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 So, to count such trios, we count the number of triples where two edges form a path of length 2 (i.e., a "V" shape), and the third edge is absent.

📌 We identify all such "V-shaped" trios in the graph with 5 nodes and 3 close pairs.

📌 Let the 3 close pairs form a path: \( A - B - C \). Then the pairs are \( AB, BC, AC \), with only \( AB \) and \( BC \) close â so 2 close pairs, 1 non-close (namely \( AC \)). This trio counts.

📌 Any other configuration of 3 close pairs that does not form such a path?

📌 Try a star: \( AB, AC, BC \) â but thatâs 3 edges all connected to B â actually forms a triangle. Then every pair is close: 3 close pairs â violates our "exactly 2" condition.

📌 Can we have a non-path configuration with exactly 2 close pairs?

📌 Example: close pairs: \( AB, CD, DE \). Then the trio \( B,C,D \): pairs \( BC \) (not close), \( CD, DE \) â only 2 close: \( CD, DE \). So this trio has exactly 2 close pairs and 1 non-close.

📌 But this is not a path of length 2 â itâs a chain of 3.

🔥 Popular Posts

$ r \geq 1 $, $ b \geq 1 $, $ g \geq 1 $
$ r + b + g = 5 $
$ r \leq 8 $, $ b \leq 6 $, $ g \leq 4 $
We list all such combinations:
$ (r, b, g) = (1, 1, 3) $
$ (r, b, g) = (1, 2, 2) $
$ (r, b, g) = (1, 3, 1) $
$ (r, b, g) = (2, 1, 2) $
$ (r, b, g) = (2, 2, 1) $
$ (r, b, g) = (3, 1, 1) $

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