🧠The equation that most people can't solve, even Harvard applicants🧠

​[00:00] 🔢 Introduction & Equation Setup — Modifying exponents and setting up the problem. ​[01:03] 🔄 Variable Substitution — Transforming the expression into a cubic equation (x^3 + x^2 + x = 155). 02:58] 🧩 Splitting Constants — Rewriting 155 as 125 + 25 + 5 to prepare for factoring. ​[04:15] 📐 Algebraic Identities — Applying difference of cubes and difference of squares formulas. ​[06:36] ✖️ Factoring — Factoring out (x - 5) and simplifying the polynomial. ​[07:49] 🧮 Finding Roots — Solving individual factors to find the real root (x = 5). ​[09:01] 📉 Discriminant Test — Checking complex roots using the discriminant formula (b^2 - 4ac). 11:03] 🎯 Solving for k — Substituting back to find the final value of k (5^{30}). ​[11:57] ✅ Verification — Testing the solution to confirm it satisfies the original equation. #Math #Harvard #MathPuzzle #Algebra #Calculus #MathChallenge #Stem #Education #Smart #MathTricks #ProblemSolving #Mathematics🤔If you want to grow in mathematics, here are these playlists :Equations with artifice 👇   • Brain-melting equations with crafty tricks🤔🤔   Entrance exam questions 👇🏻   • Admission exam questions🧠   Exponential equations with logarithms 👇🏻   • Exponential equations solved using logarit...   Lambert W function 👇   • Equations with the Lambert W function🤔   Mind-bending shaded area problems Mind-bending shaded area problems 👇   • Brain-teasing shaded area problems😫   pectacular shaded areas 👇   • Shaded areas that will drive you crazy🧠   Math monster 👇   / playlist   ​#HarvardMath ​#HarvardChallenge ​#HarvardQuestions ​#HarvardExam ​#HarvardAlgebra ​#HarvardLevel