Testing pentagonal numbers

🫧 Open on Bubbles The n th pentagonal number P n is the number of dots in diagrams like those below with n concentric pentagons. We have the formula P n = (3 n ² − n )/2 where n is a positive integer. If n is an integer but not positive, the equation above defines a generalized pentagonal number. If you’re given an n , you can easily compute P n . But suppose you’re given a large number x . How would you determine if it is a pentagonal number? And if it is a pentagonal number, how would you find n such that