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A NICE algebra problem

🎥 Can You Solve This Algebra Challenge? In this video, we tackle a fun and challenging algebra problem step by step! Here's what we're working with: Given: 1. \( a + b + c = 4 \) 2. \( a^2 - b^2 + c^2 = 10 \) 3. \( a^3 + b^3 + c^3 = 22 \) Question:What is the value of \( a^4 + b^4 + c^4 \)? 🔍 Approach: We'll break this down systematically: Use the given equations to find relationships between \( a \), \( b \), and \( c \). Explore symmetry and substitutions to simplify the problem. Apply identities for sums of powers (like \( a^2 + b^2 + c^2 \) and \( ab + bc + ca \)) to unlock the solution. 💡 Key Steps: 1. Square the first equation to find \( a^2 + b^2 + c^2 + 2(ab + bc + ca) \). 2. Combine with the second equation to isolate \( b \). 3. Use the sum of cubes formula to relate \( a^3 + b^3 + c^3 \) to \( (a+b+c)^3 \). 4. Solve for individual variables or patterns leading to \( a^4 + b^4 + c^4 \). 🧩 Spoiler Alert: The final answer is revealed at the end, but try solving it yourself first! 👍 Like, Subscribe, and Comment: Did you find another way to solve this? Share your thoughts below! #MathPuzzle #Algebra #ProblemSolving #MathChallenge #LearnMath #maths #mathtricks a Very Nice Math Olympiad Radical Problem anice algebra problem basic math olympiad hard algebra problems how to do math olympiad math olympiad questions american math olympiad algebra olympiad problems cbse maths olympiad math olympian ecuaciones funcionales resolución de ecuaciones funcionales problemas de matemáticas matemáticas avanzadas funciones matemáticas preparación para competencias ecuaciones para concursos matemática para estudiantes problemas funcionales mathematics how to solve this problem how to solve algebra algebra problems trigonometry Exponent Exponent problem find x find all values of simplify Simplification power of simple math Olympiad Olympiad math Algebra Aptitude Question Japanese math Olympiad maths Olympiad France math Olympiad math Olympiad olympiad mathematics math olympiad algebra #matholympiad​ #simplification​ #exponents​ #viralmathproblem​ #howtosolve​ #mathematics​ #viral​ #mathematicslesson​ #math​ #shasir​ #canyousolvethis​? #olympiad​ #mathematics​ #mathtricks​ #matholympiadquestion​ #funofmathematics​ #algebra​#exponential​ #olympiadalgebra​ #exponentialequation​ #education​ #equations​ #mamtamaam​ #imo​ #imoexam​ #matholympaid​ #algebra​ #mathematics​ #mathbooster​ #matholympiad​ #mathematics​ #premath​ #sybermath​ #superacademy​ #learncommunolizer​ #blackpenredpen​ #olympiadmathematics​ #matholympics​ #mindyourdecisions​ #solveforx​ #mathproblem​ #mamtamaam​ #matholympiadproblem