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📰 Solution: Square both sides: $ x^2 + 2 + \frac{1}{x^2} = 25 \Rightarrow x^2 + \frac{1}{x^2} = 23 $. Multiply by 2: $ 2x^2 + \frac{2}{x^2} = 46 $. Final answer: $ \boxed{46} $.Question: In a sustainable desert agriculture project, the combined water efficiency of two systems is modeled by $ a + b = 10 $ and $ a^2 + b^2 = 58 $. Determine the total water efficiency cubed, $ a^3 + b^3 $. 📰 Solution: We start with the given equations $ a + b = 10 $ and $ a^2 + b^2 = 58 $. First, we compute $ ab $ using the identity $ (a + b)^2 = a^2 + 2ab + b^2 $. Substituting, $ 100 = 58 + 2ab $, so $ ab = 21 $. Next, we use the identity for $ a^3 + b^3 $: $ a^3 + b^3 = (a + b)^3 - 3ab(a + b) $. Plugging in the values: $ a^3 + b^3 = 10^3 - 3 \times 21 \times 10 = 1000 - 630 = 370 $. Thus, the total water efficiency cubed is $ \boxed{370} $. 📰 Question: An organic chemist synthesizes a compound with molecular formula $ C_nH_{2n} $, where the ratio of carbon to hydrogen atoms satisfies $ \frac{a}{b} = 3 $ and their sum is $ a + b = 16 $. Find the value of $ a^2 - b^2 $. 📰 Top Roblox Gamers 4532499 📰 Bank Of Anerican 📰 Tradingview Tlry 📰 Shock Moment Trump Rfk Tylenol And The Truth Finally 📰 Ie11 For Windows 7 32 Bit 📰 Induction Vs Electric 📰 Excel Function For Minus 📰 Step By Step Alternate Row Colors In Excel No Formulas Neededeasy As 1 2 3 3606484 📰 You Wont Believe How These Christmas Inflatables Shock Everyone This Season 4381610 📰 A Rectangular Field Has A Length That Is 5 Meters More Than Twice Its Width If The Perimeter Of The Field Is 70 Meters What Is The Width Of The Field 6867266 📰 Is There A Way To Get Free Robux 9479872 📰 Breaking News 5 G Home Internet And The Internet Goes Wild 📰 Bank Of America Acushnet Ave 📰 See Why Collectors Cant Get Enough Of The 2002 Mustang Gtheres Its Secret 9592613 📰 Bmw Of Birmingham 2647622