hello let's do some math for fun you have this question for you guys and this question inspired
by brilliant the original version of this is with 2016 but we are in 2020 already so change to 2020
right by the way do not suffix right here because we are trying to compute this is pressure if you
software X right here and a plugging the excellent tool here that's not going to be pretty nice but
anyway as always please pause the video and try this first all right hopefully gets a chance to
try it here we see we have the 6x power and this is negative 6x power it seems like we should
just go back to the original equation and raise both side to a sixth power and hooked on to that
neither that's going to be pretty bad on the left hand side instead of this right here actually can
be factored it and we are going to do that but I do not want to write down 2020 2x power so many
times so that's to the following I'm just going to do a substitution I was a lead of variable let's
say you because I like you head I will be calling this to be xx xx to the X power so the original
equation becomes u plus U to the negative one that's equal to 3 and this expression is going to
be the square root and here we have just U to the sixth power and then minus U to the negative sixth
power over you and a minus U to the negative one power like this and that's what we have to compute
all right so now let's see what we can do with this have a look this right here is the difference
of two six powers so we can look at this as the difference of two squares was the difference of
two cubes it's easier to look at this as the difference of two squares and then we factor
it if you want to do the other way in favor video alpha D is kind of tricky so checked out you would
like anyway here we are going to look at this as the following we will just break this down so
difference of two squares so that means the first term is U to the third power and then we will have
to - you to the negative third power like this and then we have another one which is you to the third
power plus U to the negative third power like this alright and then this is divided by that
denominator which is u minus U to the negative one particularly so far and they made you more
visible for you guys better all right now what can we do next what just keep factoring and a whole
foot best right so right here let's see if I can fitting everything right here in fact this is not
the first time recording this because the previous times I fail I'm fitting everything onto the port
so life as a youtuber with small ports anyway this right here factory as the difference of two cubes
the first factor is going to be U to the first power and then minus U to the negative one power
and then we will have to do the following this is going to be u square and then Plus this times
that you to the third power times due to negative third power is just equal to one so we have to add
one to it and then in the end we have to add the U to the negative one power square which
becomes U to the negative two so that's what we have and this is actually pretty good because on
the bottom we really have this which is u minus U to the negative one yes this is wonderful because
we can use the blue marker to cancel this out all right so now I just have to factor this right here
which will end up with u plus U to the negative one and that's what we have and then right here
see again I've failed you again so I will try this I will just indicate with an arrow factoring this
right here we will end up with u square and then we have to subtract this times that which is just
1 which is similar than just due to the negative two so this goes here all right that's your P okay
now let's see what else we can do we do know this though this right here is our street right here
so that's good and the problem is that what should we do this and that how to utilize this idea well
the good thing is that things can happen with the blue marker this right here can should be factor
anymore and the better thing is we can squeeze out this to help us out so check this out note
right here so I'll just put this down in blue for you guys when we have u square plus let me write
this down first which is U to the negative two and then plus one this right here it's actually
the same as a we can actually complete a square with the first two terms because it does look like
a perfect square almost here this is how we do it right here you see this is the same as saying you
Square and down plus something and then then we just keep a space plus this right here it's the
same as U to the negative one squared right if you want to get a perfect square right here with
stop passing the middle and the reason I wanted class is because I want a plus right here in the
middle I will have to have two times this and that namely u times U to the negative one and then W is
to have the plus one after that but you see this right here it's actually just a two so in fact
from here to here we're just adding it right here to complete the square but you cannot just add
two of course you have to just come back here and then minus two so that this and that can so shut
up right and with stepping that these three terms will just keep us u plus U to the negative one and
then raised to the second power and of course 1 minus 2 we end up with minus 1 so this right here
is going to be going for at better yet do we know the values yes we do u plus u 2 negative 1 this
is nice T equal to our street right here so this is 3 square minus 1 and work that out you get 8
great similarly for this factor here if you look at u square and then again plus huh that's read s
plus U to the negative 2 but here we have minus 1 well what do we do this right here is U square and
then just leave a space plus u 2 negative 2 right here you know we have to add the 2 just like this
in here we have the negative 1 but again similar reason we have to just minus 2 right here that's
the idea well here on all we just end up with u plus U to the negative 1 square again and this
and that will give us minus 3 which is very nice all right put the street right here so we have 3
square minus and under 300 this right here is just going to give us to be 6 very good huh so
that's pretty much it we have all the stuff that we need first this right here is 8 so I'll just
put that down to be blue this right here is our 3 so we have 8 times 3 now and lastly this right
here is the 6 that we have so multiply it by 6 well 8 times 3 is 24 24 times 60 is 144 all
together take the square root after that we end up with a nice 12 so the instance of this right
here is equal to 12 all right if you enjoyed the question that we just did they I think you
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