Peru | A Nice Algebra Problem | Math Olympiad

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Find the value of x?
How to solve x^x-2 = x
In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation x^x-2 = x in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[@MananArhamOP]

The best teacher to ever exist on RUclips.

[@SALogics]

Thank you so much! ❤

[@LITHICKROSHANMS-gw2lx]

Super solution sir

[@SALogics]

Thank you so much! ❤

[@dumitrudraghia5289]

Dacă ai metoda 2, de ce mai umbli pe slte cărări încurcate?!

[@SALogics]

Pentru că metoda 1 este mai interesantă! ❤

[@YAWTon]

There is an obvious solution x=3. It is equally obvious that there is a second real solution (this follows from the convexity of 3^(x-2) and the behaviour of the exponential function as x goes to +oo and -oo). Without the 2nd solution, this is never a Math Olympiad problem. The approximate numerical value of the second solution can be found by numerical methods, x~0.1279, or analytically using Lambert's W (c.f. @prollysine's comment).
It is always a good idea to think about the number of solutions, how do the functions involved in the equation behave when x goes to plu or minus infinity, are the functions, monotonic, convex, ...

[@SALogics]

Thanks a lot! I will find this solution too next time. ❤

[@anestismoutafidis4575]

3^(3-2)=3^1=3 x=(9)^1/2=3

[@SALogics]

Very nice! ❤

[@prollysine]

-ln3/9 = -ln3*x*e^(-ln3*x) , trick , -ln3/9 * 3/3 , -3*ln3/3^3 = -3*ln3*e^(-3*ln3) , --> -3*ln3= -ln3*x , x1=3 , test , 3^(3-2)=3^1 , 3^1=3 ,
x2=W(-ln3/9)/-ln3 , x2=~ 0.127869 , test x1 , OK , test x2 , OK ,

[@SALogics]

Very nice trick! I really appreciate that ❤

[@prollysine]

@@SALogics Thanks!

[@habeebalbarghothy6320]

Second method is easier

[@SALogics]

Yes, of course! ❤

[@АндрейАнцышкин]

😅х=3 моментально ❕

[@SALogics]

ты прав! ❤