A nice Exponential problem | Square root Simplification | find x

Support me plz Subscribe the Channel
#lklogic#integral#maths#olympiadmathquestion#algebra#exponentialequation#exponents#vedicmaths#integral#how#lesson#mathsclass#viral#lklogic#viralmathproblem#howtosolvemathspuzzles#howtosolveolympiadmathproblem#mathematics#mathematicslesson#matholympiad#internatinalmathoympiad#matholympiadequation#premath#sybermath#mathwindow#greqants#mathstudent#mathtrick#mathshorts#mathrubhuminews#ssc#ssccgl#upsc#upscaspirants#upscpreparation#mdcat#engineermuhammadalimirza#upscnotes

[@jronic]

It's always nice to see someone making such videos. Though, some remarks:
1. The way to find the solution is needlessly complicated.
x = sqrt(x) + sqrt(x) = 2 sqrt(x) = sqrt(4x)
Is equivalent to (note that x must be non negative to restrict ourselves to real solutions anyway) x² = 4x.
Now note that 0 may be a solution and proceed for the other case where we then can divide by 0 which instantly results in x = 4. So there is your result, x in {0, 4} solves it.
2. The way to double check makes me, well, furious. It's good practice to do so, don't get me wrong. But everytime I see people replace x on both sides of the equation and put an equals sign between it, and THEN simplify, it makes me sad.
Either start with one side and simplify (and potentially complexity again) to end at the other side of the equation. Or for God's sake make clear (and sure) that you are talking about equivalences, by putting between the equations.
Starting with something that you want to check, do something to the equation and land at something true (through implications) is neither a proof nor a check of your result (ex falso quod libet).
Just had to write this, I feel better now, thanks 😅