x^x = x, Find x? Only 1% solved This Tricky Olympiad Question | Math Doctor

Can you solve this tricky Olympiad question? Question: If x^x = x, Find x? In this video Math Doctor solves the famous equation x^x = x step by step. Most students say only x=1, but there is a second hidden answer! We use the law a^0=1 and x^(x-1)=1. Solution: x^x = x ; x^x / x = 1 ; x^(x-1) = x^0 , x-1=0 , x=1 AND also check x=-1: (-1)^(-1) = 1/(-1) = -1 ; x=-1 also works! Final Answer: x = 1, -1 What you will learn: Laws of Exponents: a^0=1, a^m/a^n = a^(m-n) How to solve x^x = k type equations Why we must check negative case Chapter / Topic: Class 7: Exponents and Powers Class 8: Exponents and Powers - Laws of Exponents Class 9 & 10: Number System, Polynomials - Exponential Equations Class 11 & 12: Relations and Functions, Exponential Functions Boards: CBSE, ICSE, IGCSE, IB, Cambridge, State Boards, NIOS Exams Where This Type Comes: Math Olympiad | IMO | RMO | INMO | PRMO | IOQM | NIMO | Math Kangaroo | UKMT | AMC | NTSE | SAT | ACT | JEE Mains | BITSAT | CAT | SSC CGL | UPSC CSAT | CUET | IPMAT Comment your answer first! #MathDoctor #OlympiadMaths #xxequalsx #exponentialequation #olympiadmaths #mathstrick #exponentsandpowers #mathdoctor #cbse #icse #ioqm #imo #satmath #jeemaths