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πŸ“° We want positive ratio. Try $ y = \frac{-7 + \sqrt{7}}{9} \approx \frac{-7 + 2.6458}{9} = \frac{-4.3542}{9} \approx -0.484 $, negative. Other root: $ \frac{-7 - 2.6458}{9} < 0 $. Both negative β€” meaning $ A/d < 0 $, so first and last have opposite signs β€” impossible for $ A^2 + (A+3d)^2 = (sum)^2 $ unless not ordered. πŸ“° Wait β€” the original assumption about ordering may be wrong. Try symmetric AP: let the four terms be $ a - 3d, a - d, a + d, a + 3d $ β€” symmetric around $ a $. This is a valid arithmetic progression with common difference $ 2d $, but we can scale. Define as AP with common difference $ 2d' $, but to match convention, let common difference be $ 2d $, so terms: $ a - 3d, a - d, a + d, a + 3d $. Then first: $ a - 3d $, last: $ a + 3d $, sum of squares: $ (a-3d)^2 + (a+3d)^2 = 2a^2 + 18d^2 $. Sum of all: $ 4a $, square: $ 16a^2 $. Set equal: πŸ“° 2a^2 + 18d^2 = 16a^2 \Rightarrow 18d^2 = 14a^2 \Rightarrow \frac{d^2}{a^2} = \frac{14}{18} = \frac{7}{9}. πŸ“° You Wont Believe These Hidden 401K Withdrawal Rules Fidelity Secretly Reveals 4146113 πŸ“° Conbunn Cardboard 1807395 πŸ“° Calypso Cafe 5190521 πŸ“° Goofy Gorilla 2168197 πŸ“° This Minecraft Pocket Game Will Change How You Play Forevertry It Today 8674128 πŸ“° Millicents Prosthesis 6975762 πŸ“° Al Doug Jones 4406975 πŸ“° Unlock The Secrets Behind Geography Wordle With This Hidden Word Power 1734530 πŸ“° Wnba All Star Game Rules 3152058 πŸ“° The Untold Story Of Eddie Guerreros Death How One Wrestlers End Changed Wrestling Forever 750384 πŸ“° You Wont Believe How Papalo Transformed Cooking In 2024This Herb Is A Game Changer 447551 πŸ“° Metropole Hanoi Vietnam 8420767 πŸ“° Camera For Vlogging 4188406 πŸ“° Sorprndete Con Este Recordazo De Feliz Cumpleaos Aun Hermanono Te Lo Pierdas 4734316 πŸ“° This Quartters Intel Earnings Report Could Change 9911077