okay we are going to solve this equation but we are not going to square both sides because
you if do that on right hand side we get x to the fourth power term so that's not good that's
bad that's dangerous in fact that's a trap so here's the idea we see we have five minus x up
the square root ends if I minus X square and here's idea hopefully guess I see my video on
the internet nasty in my control that's because that's how we're going to it right yeah I'll move
this to the house I move this to here you'll see why this is going to be x squared that's equal
to five minus that square root of firemen's X and of course I can just take the square root on both
sides of course don't forget the plus minus and we can cancel this out and in fact this equation it
does have two students because if you graph this right yeah you get this and you can grab this and
get that and of course you see two intersections so you have two solutions that's why you have to
really consider in the plus/minus so let me just write this down with your X is equal to the past
version of the square root of pi minus a square root of 5 minus X and then on the other hand
let me just write our X is equal to negative version of the square root of the PI minus the
square root of 5 minus X like this and now I was just ready stung again in read off so we get X
is equal to square root of pi minus the square root of 5 minus X white won't do that because
Bryce here you see here we have these eggs I can put this down right here for this X so you see X
is actually nothing but just the square root of the 5 minus the square root of 5 minus X because
X is now that's I can plug in so it's minus the square root of 5 minus square root of 5 minus x
max it's what I can just plug in this into itself right so have the - school of fire and song song
song so I can just put on top that I like this and hopefully gets don't might well right here
I will use a purple pen because now I see this part is nothing but just this expanding purple
so if you like to actually write this down as follows this is just x equals 2 square root of 5
minus this purple X which is really cool isn't it and now we can of course continue can square both
sides so we get X square and of course that's move this than that well that's how they get
plus X minus 5 and this is equal to 0 this is the quadratic equation has two solutions power
just kept on the party version because right here is passage right so keep on the positive version
and of course you just watch ready for my X is equal to of course do the negative B which is
negative 1 and then just at square root of b square which is 1 squared and a minus 4 times
this times that you get 20 and you pretty much do one plus 20 you get 21 right here or over 2
times that which is 2 times 1 which is just 2 and this is the first answer right here and now let's
check this out this is really cool well well of course I'll do the same scene I was just put on
X is equal to negative version of the square root of 5 minus the square root of 5 minus X
like this of course you see here we have this executed I will put this down right here for
that so we see that X is nothing but just a power this is negative square root of 5 minus square
root of 5 - well this X is negative so minus - of course this becomes plus and then of course
you have the square root of 5 minus the square root of 5 - right but X is negative so in fact
this becomes plus and then of course you can just pretty much have this and so on and so on and in
fact this is like alternating term Oh nested radical really cool but how do we do this well
of course that's used a purple pen again right here let's just focus on this part right here so
I will make a note on the side for you guys this is how we can do it whenever you have a infinite
nested radical if he alternates it's just like this suppose of a and then minus square root of
a plus square root of a minus square root a and so on so on like this in fact you have a really
really nice formula this right here you can just write it down square root of 4 a minus 3 minus
1 over 2 like this and of course I'll probably prove this to you guys on the other time so for
the other time part like here it's just 5 so you see this X is just equal to negative and oh this
is just by this formula now so you can just plug in 5 for the a and of course 4 times 5
is 20 - magnetize them and think inside the square root so the square root of 17 minus 100 / - like
this and that's for this part right and of course if you want to be Q because we are Q so I can't
distribute a negative so in fact in yeah yeah let's put on negative 1 first negative negative
1 which is positive 1 and then negative 70 instead of the square root and / - like this and with that