Waching daily Dec 31 2018

Two-square, two-square, two-square equations

square times or something like that, two-squares.

quadratic, twice. "x" to the fourth, but

in a special way. Come on, let's see

this.

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The bi-square or bi-square equations

quadratics can be written in your

general form of this form: ax a la

fourth plus bx squared plus c equals

zero.

Yes, sir, yes, sir, yes, ma'am. As you can see

this is pretty much like the

quadratic or second equations

degree only that these are elevated to the

square. Look, see?

are very similar. Well, they are so

similar that we can even apply

the same resolution methods.

Methods of resolution for this one? therefore by

example for the second equations

degree is often used the famous

formula, the formula of resolution that

it would be this: less b, less b, more less

root of b square minus 4ac split

of 2a, 2a.

Well, well, that's what we're gonna do.

to use to solve our equation

two-square. The two-square equation that

we're going to solve this is going to be it:

"x" to the fourth minus 4x to the square plus

3 equals 0.

But before we start solving this.

We have to ask ourselves a question.

fundamental: What does this mean of

solve a bicuadratic equation or bi

square? Aha! Well, let's see what it is.

this. So solving this equation is what

next:

I have a function that is "x" to the fourth.

minus 4x plus 3. I have this function (like

you see is very much related to this

equation) I have this function and this

function could be represented in the

Cartesian axis. And if I represented her,

if I represented her, it turns out that the

graphic of this function was going to cut

at some points to the "x" axis. Yes,

Look,

if I represent this function that there is here

I'd have this drawing, you guys, see? The

drawing would be this for this function

we're doing. Well, well,

it would be something like that, as we just saw,

it would be something like that. Well, solving this

equation would be to find these points,

would be to find these points. Let's see

that this equation has four

solutions. Well, the four solutions

are each of these points, points in

where this function,

his graph, cuts off the "x" axis. Aha!

This is solving an equation, specifically a

two-square equation. Well

let's get to work.

the first thing we're gonna do is gonna

to be a change of variable. In mathematics,

in the equations, many times it is

easier, it is easier, for example if

we have "x" squared

because it's easier to do the following:

we say "for the sake of convenience we are going to define

next, let's say "x" to the

is equal to, for example, a "t", a

another variable. The "x" squared we go

to call "t." What if we do this one

change? (well, this sign means "by

definition". If, by definition, we say that

"x" squared is "t" then our

two-square equation we can write it

in this way: square "t" minus 4t plus 3

equal to 0, equal to 0. Yes, yes. Yes, yes. I'm going to

erase all this stuff in here, I'm gonna

erase all this stuff that's here and

let us patiently solve this equation

of the second grade by the famous

formula.

For any second degree equation

What's he got, what's he got this way.

because its solution is given by the

the following formula,

by the following formula: it would be less "b"

more less root of b to square less 4ac

2nd game. Boys this formula

it doesn't come down from the sky this formula

has its foundation. If you want to see how

this formula is deduced, please, by

please, go to this video here and

you'll see how it resolves. The fact is that

we're going to apply it right now.

As you see, as you see

In our case "a" is worth 1, "b" is worth minus 4, "c"

is worth 3 and substituting these values in

this formula we can write and

we write, less "b" then less, less

four, plus minus root

of "b" square. "b" square? Well, minus 4 at

square mutiplicated by minus 4ac. Minus 4, "a" is worth 1

and "c" is 3, "c" is 3,

2nd game. "a" is 1.

Come on, let's operate quickly. We operate quickly...

but okay, sure.

We've got four plus minus 16 root.

-12. All right, all right.

we have here then 4 more less

root of 4 match of 2. This there is here

I'm gonna take it off, I don't need it, I don't need it.

I need it now. And look at this is the same, this

is equal to

4 more less, 4 more less... root of 4? then root of 4 is

two, plus minus two and here I'm going to get

two solutions. I'm going to get a "t" that

value 4 plus 2 is 6 and 6 divided between 2 is 3 and another

solution of "t" will be 4 minus two is two, two

between two is 1. Boys, girls we have

two values for "t", we have two values

for "t," but look, it turns out "x."

square is equal to "t" so we will have

that "x" square is equal to 3 and we will have

that "x" square is equal to 1,

olive.

Let's make room. Let's make some space.

space here and taking into account that "t"

is equal to 3 we can write that, by

example, "x" square is equal to 3 and also

we can write that "x" squared is

equal to 1. Boys, then we have here two.

equations that need to be solved as well.

Let's see this one. "x" square equals 3.

Well, then "x" equals more or less.

root of 3.

A lot of care, a lot of care with

"yum, yum, yum" eat you the minus sign, this is

what you're used to writing many, many times.

and it's more but it's also less. Very much

Be careful, this is one of the most mistakes

typical. Careful. To see very typical errors

you can go to this video and you'll see that this

It's number one, number one.

of the errors and on the other hand

we have here that "x" equals more minus

root of one who is one.

Okay. [Chuckles] Conclusions, friendly conclusions and

girlfriends.

We have the following solutions: a

solution is root of 3, another solution is

less root of 3, another solution is 1 (let's go to

to say "x" sub 3, "x" sub three, we are going to do well the

3, so) and another solution will be "x" sub 4 the same

one positive, no, 1 positive, 1 negative.

Well, these are our solutions.

Come let us represent to finish a

little of this that we've obtained. We will

to make a representation understanding

Well, what have we done in the past?

these minutes.

We have here our solutions is

I mean, if we take every one of these.

solutions and bring them to our

bi-square equation we'll see that the

equation is satisfied because they are the

solutions but what does this mean, that

does it mean to have these solutions? Well

as we said at the beginning,

we start from one, from one function

which is the following: "x" to the fourth minus

4x square + 3 and this function we can

represent it in the Cartesian plane.

If we represent it, this is the axis of

the "Y" this is the axis of the "X", if

we represent them

we'd see that he more or less has the

next aspect, more or less has the

next aspect. Well, these solutions,

these solutions, these points that there are

here would be these, would be these that I'm going to

draw. Well, I would have for example here

less than 3 root

would have here, for example, at least one.

I'd have here the 1, sorry, it's not very

symmetrical but we realize what

which means and lastly would have here

root of 3.

Well boys, well girls ... colorín

colored this exercise is over.

bi-square equation without any type of

problems we have all the solutions

you see? 1, 2, 3, 4. Many times it doesn't happen

this, many times we have only three,

we only have two or we don't even have

none, but we have them all. Well

See you soon, see you soon. Next

video of quadratic equations now

the same. See you later.

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