Math Is Fun Forum

technique09

Member

Registered: 2008-10-04

Posts: 14

This has been bugging me...

For some reason i cannot seem to get the answer to this.

Express (x)^4 - 4(x^2) +16 in the form

(x^2 + Ax + B) (x^2 +Cx + D)

What i tried to do is to expand  the two brackets above out and equate coefficients, however i couldnt get the right answer i kept on getting +4(x^2).

Can anyone suggest another possible way of doing it that works?

Thanks

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

  (1)
from here we see that

     (2)
Now if we multiply all the terms in the brackets,will have

  (3)
From (1),we can notice that we dont have just x alone,without exponent,so it means that in the equation all terms that have x should be "elminated",so:

          (4)
Now we use the same methode with

                   (5)

We can substittue (5) in (4),and we'll get:

            (6)

Now from

Now if we su8bstittue all these values in (3),we will get:

Now if we collect the terms we'll get:

Now from the formula in the beginning,

we see that we have just 

,so

Now the solution is 

Last edited by G_Einstein (2008-10-06 00:12:20)

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

technique09

Member

Registered: 2008-10-04

Posts: 14

Re: This has been bugging me...

Excellent post G_Einstein, it helped me alot. I got  up to part (6) by myself, but what you did after that was clever, putting everything in terms of A.

However i do have a few questions regarding your method.

1) From B^2=16 how did you know B=4 and D=4? Couldnt they both be -4? I had trouble determining whether they were positive or negative.

2)Once you collected like terms i think you made a mistake when writing 4(x^2) - (A^2)(x^2)= -4(x^2), i think it should have been 4(x^2) - (A^2)(x^2) + 4(x^2)= -4(x^2), i think you accidentally missed the plus four x squared.

The solution you wrote was also wrong, firstly you missed the x on the root 8, and secondly its root 12x.

I think the solution is [(x^2) + (12^0.5)x + 4] [(x^2) - (12^0.5)x +4]

Thank you very much G_Einstein, your method past part (6) was clever, i should have thought of it!

PS How do you write your maths in that format?

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

Hmm,Imy first result was also

but when I substittue the result was wrong,but when the result was then

,I subsstitue and it match!!!

May be I've done some mistakes,bevause if you want to write math in that format,when you want to write a formula,just "push" the bouton "math" above the rectangle in wich you write the reply,and between the two "maths" write the formula,but in the correct form,in the form that Latex(program) understand them,it's like almost the same fomre of what you've wrote before,for example for

you just write x^3

Look again,and try to multiplicate all the terms of the result and look if you win

I will look the mistakes that I've made and I'll correct theme,but I can't do it righjt know because I must go,and for the

I just took 4 because maybe,with -4 it doesn't match at the end.I will try also with -4 and I'll see what I'll get.
I'll write you again with an answer in this topic.
Bye

PS The esence of resolving math problems is to use the simple logic with numbers and to think,what we've got and what not,what do we need to resolve the problem.Everything goes with logic

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

Yes,you were right,in my paper I wrote that,but when I wrote in the reply,I accidentaly missed the -4x^2.
About the answer I'll see again about

,because when I multiplyued,the result didn't match,so I'll recomend you,try multiplying all the terms and get just 3 nomous,but not

,try with

I'll ee about the other question,because I replyed you just a few seconds after the anterrior reply.
I'll see them later because I must go.
By the way,in which grade are you???

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

technique09

Member

Registered: 2008-10-04

Posts: 14

Re: This has been bugging me...

Thanks again G_Einstein, what you wrote has helped me alot, the problem became much clearer to me, once i saw your method, to be honest i should have got the answer, i wasnt thinking enough.

PS The esence of resolving math problems is to use the simple logic with numbers and to think,what we've got and what not,what do we need to resolve the problem.Everything goes with logic

That makes a lot of sense, and i will think about it when tackling problems. Im quite sure

works, i think you just made a mistake in not considering the extra

. However, your method was good and it helped me alot! Thanks also for telling me about the "Math" Button, it shall make my writing neater in the future!

Ive just started my first year at uni. What level of maths are you studying?

Last edited by technique09 (2008-10-06 09:46:02)

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

Now I'm in the 12-th grade,gymnasium(High school),mathematic-informatic department

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

technique09

Member

Registered: 2008-10-04

Posts: 14

Re: This has been bugging me...

Excellent, you are bright for your age. How old are you? and where are you from?

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

Byt he way,how old are you???

Last edited by G_Einstein (2008-10-08 01:41:49)

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

technique09

Member

Registered: 2008-10-04

Posts: 14

Re: This has been bugging me...

im 18, how old are you?

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

I don't know what happent,because I wrote a post were I said that I'm 18 years old,I'm from Mitrovica(Kosovo) but I think that I made a mkistakes,I edited it and I deleted the previous text.
Have you ever heard about Kosovo?
Where are you from?

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

technique09

Member

Registered: 2008-10-04

Posts: 14

Re: This has been bugging me...

Yes i have heard of Kosovo, i have some friends from there. Im from London. Are you currently studying in University?

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: This has been bugging me...

No,I'm not studying at University.
I'm in 12th graed,in gymnasium(High school)

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.