【慶應高校】式変形のセンスが問われる一問

#KeioHighSchool #HighSchoolEntranceExamMath #TransformingEquations #CompletingTheSquare #CalculationProblems ■ Problem KeioHighSchool (x+y)^2 = 30 + 12√6 (x-y)^2 = 30 − 12√6 In this case, (2x+3y)^2 + (3x-2y)^2 Find the value. ■ Approach Find x^2+y^2 and xy from (x+y)^2 and (x-y)^2 Finally, expand and summarize the equations. ■ Basic Equations (x+y)^2 = x^2 + 2xy + y^2 (x-y)^2 = x^2 − 2xy + y^2 Adding the two equations gives: 2(x^2+y^2) = 60 Therefore, x^2 + y^2 = 30 Subtracting the two equations gives: 4xy = 24√6 Therefore, xy = 6√6 ■ Equation to be Determined (2x+3y)^2 + (3x-2y)^2 Expanding each gives: (2x+3y)^2 = 4x^2 + 12xy + 9y^2 (3x-2y)^2 = 9x^2 − 12xy + 4y^2 Adding gives us 13x^2 + 13y^2 ■ Calculation 13(x^2 + y^2) = 13 × 30 = 390 ■ Answer 390 ■ Summary ・When the squares of the sum and difference are given, add and subtract. ・The key is to decide whether to use xy or not. ・Finally, realizing the symmetry will dramatically reduce the number of calculations. 🔗 Related Videos & Recommended Links [Junior High School Entrance Exam Math Calculation Problem Explanation Series] ▶    • 灘中入試問題 2005年度1日目｜素因数分解で分数の計算問題   [Junior High School Entrance Exam Integer Properties Practice Problems] ▶    • 【魔方陣の攻略法】真ん中の数の見つけ方！公務員試験＆中学受験の数的処理対策｜算数過去...   [Kaisei Junior High School Entrance Exam Questions and Past Exam Explanation Series] ▶    • 【開成中学の算数】単位分数の和と整数問題を徹底解説！2010年度過去問に挑戦｜中学受験算数   [Nada Junior High School Entrance Exam Questions and Past Exam Explanation Series] ▶    • 灘中入試問題 2005年度1日目｜素因数分解で分数の計算問題   📢 A Request to Viewers If you found this video helpful, please let us know by "Like" or "Commenting"! Requests for other questions you'd like us to explain are also welcome. 📌 About This Channel This channel offers fun ways to learn arithmetic and math while steadily improving the skills needed for exams. We fully support everyone who wants to hone their thinking skills and overcome their weaknesses! 📩 Job Requests/Inquiries For interviews and job inquiries, please contact: 📧 [email protected] #JuniorHighSchoolEntranceExams #ExamMath #Math