Math Is Fun Forum

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Need help!

OK.  If you really want to work from y.  I'll demonstrate one value for y and maybe you can do the other.

Say

times top and bottom by an amount that eliminates the square root from the bottom

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Thanks, now I have one more part I need to compute

Last edited by evene (2015-11-22 10:54:45)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

Hi;

How did you do on the last part?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Define "How did I do on the last part?"

What last part?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

now I have one more part I need to compute

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Need help with these high degree difficult problems:

(1) Simplify

(2) Write

in summation notation

(3) Prove that any 2 consecutive Fibonacci numbers

and

are relatively prime

(4) Find the sum of the infinite series

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Haven't worked on yet bobby! After all, school is my main priority

For (1) I think I have it:

And whatever that equals. I am mentally getting about

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Happy Thanksgiving to whoever is reading this and whoever is in the US!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

Hi;

1)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Ok that... looks complicated... Is it computation problem? (For my post)

Last edited by evene (2015-11-23 12:57:09)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

I used the summation calculus, it is complicated. Look for an easier way, now that you have the answer.

4)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Can you do it in a much easier method? Like, without all of the

symbols?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

4)

This is called a geometric series and there is a formula for them but I like the following trick.

Now just add and subtract the remaining fractions.

Can you do it in a much easier method?

There are lots of easier ways.

Like, without all of the

symbols?

The sigma or big E is the symbol for summation. It is not as common as the integral sign is but it is just as important. You will encounter it often, get used to it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Thanks! Hey Bob! Can you link the Sum symbol website on the Math is Fun website below when you get back out? Thanks!

Thanks Bobbym for the explanation on Q4! I'll just search up the formula for the Geometric Sequence!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

Hi;

Q2)

This is one way:

http://www.mathsisfun.com/algebra/sigma-notation.html

http://www.mathsisfun.com/algebra/seque … etric.html

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Thanks Bobbym! You probably spent a lot of time working on these questions! Now we need Q3

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

Hi;

I have nothing cleverer than this already worked proof which makes use of two properties of the GCD.

Let GCD(m,n) = (m,n)

1) (m,n)=(n,m)

2) (m,n)=(m+kn,n) where k is an integer.

http://math.stackexchange.com/questions … vely-prime

But before you go there I suggest you work on the proof yourself until you have exhausted all possibilities that you can think of.

Thanks Bobbym! You probably spent a lot of time working on these questions!

It did not take me a long time, the methods of experimental math (EM) knocked them all off in under a minute apiece. It took much longer to latex them up and try to replace concise computation with verbose classical math jargon and methods. This ain't because I am some kind of big brain, it is because EM makes short work of school problems. Funny thing is that it also works better on real world problems too, suggesting that the universe is some sort of classroom or school?!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Interesting...

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

This problem though... Seems impossible

. Find

Last edited by evene (2015-11-25 02:42:29)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

ABCD = 1089.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

I figured out that 9=10-1, so replacing 9 with that gives us ABCD0-ABCD=DCBA. Then use logic

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help!

Or you can let your machine use logic and you go sailing...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

I have a question on this:

How can this be factored by grouping?

Last edited by evene (2015-11-25 14:24:00)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Need help!

hi evene,

Like this:

To get those squared terms there must be two factors each with an x term and a y term.  To get minus y squared one must have a minus sign.  So it would take the form:

(x + y + a)(x - y +b) for some numbers a and b.  That also accounts for no xy term.

So that makes

x^2 - xy + bx + yx - y^2 + by + ax - ay + ab.

From the x coefficients b + a = -6 and from the y coefficients b - a = 4

That's enough to fix a and b.  Adding gives 2b = -2 so b = -1 and so a = -5.

This gives ab = 5 which is just what we wanted, so here's the factorisation:

(x + y -5)(x - y - 1)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need help!

Thanks Bob. I realized that you could also do that by completing the square, then subtracting the same amount that you added