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📰 Solution: Let $ t = x^2 - 3 $, so $ x^2 = t + 3 $. Substitute into the equation: $ f(t) = 2(t + 3)^2 - 12(t + 3) + 13 $. Expanding: $ 2(t^2 + 6t + 9) - 12t - 36 + 13 = 2t^2 + 12t + 18 - 12t - 36 + 13 = 2t^2 - 5 $. Thus, $ f(x^2 + 1) = 2(x^2 + 1)^2 - 5 = 2x^4 + 4x^2 + 2 - 5 = 2x^4 + 4x^2 - 3 $. oxed{2x^4 + 4x^2 - 3} 📰 Question: The diagonal of a rectangle is 25. What is the maximum possible area of the rectangle? 📰 Solution: Let the sides be $ a $ and $ b $. By the Pythagorean theorem, $ a^2 + b^2 = 25^2 = 625 $. The area $ A = ab $. To maximize $ A $, use the identity $ (a + b)^2 = a^2 + 2ab + b^2 $, but it is more direct to note that for fixed $ a^2 + b^2 $, $ ab $ is maximized when $ a = b $. Thus, $ 2a^2 = 625 \Rightarrow a = rac{25}{\sqrt{2}} $. The maximum area is $ A = \left(rac{25}{\sqrt{2}} 📰 What Youre Not Being Told About Inmate Sales The Hidden Truth Behind Prison Trade 8816671 📰 Alaska Airline Credit Card Bank Of America 📰 Bank Account Incentives 📰 Fallout Shelter Online Build Customize And Protect Your Virtual Bunker Today 5246376 📰 Major Breakthrough Missing Somebody And It Changes Everything 📰 Is This Trailblazing Shift Called Gwen Stacy Really Trans Shocking Insight Inside 4122424 📰 Recovery Of An Mmo Junkie 1574109 📰 You Wont Believe How These Dc Snipers Revolutionized Sniper Warfare 2875482 📰 My Lust Wish 📰 Best Credit Cards 📰 Found Bank 8856237 📰 Oracle Cart View 📰 How Many Days Until May 13 7035896 📰 Get Rid Of Spam The Ultimate Qq Webmail Hack You Must Try 3726519 📰 Eureka Verizon