[cricket001]

Hi, if possible could you help me out with a question. It is on core 2 ocr maths paper (not Mei) 9 jan 2008 4722/01.

the question is question 10 iii) Verify that X=2 is a root of the equation:

(2X+5)^4 - (2X-5)^4 = 3680X - 800

and find the other values of x?

Any help would be greatly appreciated, as i have the answers for this test paper but i am unable to understand how to get the answer.

many thanks

[Hopple]

'Expand' and simplify the left hand side to leave you a cubic, then divide by the root you know.

[Mr M]

Form a cubic and factorise.

[cricket001]

Hi, if possible could you rune through the steps as i am still not getting it :-(

here is the answer from the mark scheme, but id not get it

(9)^4 – (-1)^4 = 6560 and 7360 – 800 = 6560
320X^3 – 1680x + 800 = 0 4X^3 –21x+10=0
(x – 2)(X^2 + 8x – 5) = 0 (x – 2)(2x – 1)(2x + 5) = 0 Hence x = 1⁄2, x = -21⁄2

[Hopple]

(Original post by cricket001)
Hi, if possible could you rune through the steps as i am still not getting it :-(

here is the answer from the mark scheme, but id not get it

(9)^4 – (-1)^4 = 6560 and 7360 – 800 = 6560
320X^3 – 1680x + 800 = 0 4X^3 –21x+10=0
(x – 2)(X^2 + 8x – 5) = 0 (x – 2)(2x – 1)(2x + 5) = 0 Hence x = 1⁄2, x = -21⁄2

What bit don't you get? The expansion, the factorising?

[cricket001]

9)^4 – (-1)^4 = 6560 and 7360 – 800 = 6560 - uphill here i get it, but the next steps i have no idea..
320X^3 – 1680x + 800 = 0 4X^3 –21x+10=0
(x – 2)(X^2 + 8x – 5) = 0 (x – 2)(2x – 1)(2x + 5) = 0 Hence x = 1⁄2, x = -21⁄2

[TenOfThem]

I really do not understand your problem

As I said on the other post asking the same question


Expand the brackets
Simplify
Factorise

[member910132]

Expand

Using the Binomial expansion, or otherwise.

After you have expanded it, then you cancel like terms and simplify, leaving you with

- I haven't actually done this, I have just copied it form your above post.

Now you know that

, thus

must be a factor, hence divide the whole thing by the factor to see what you have left.

you could use long division for this if you want., so we have

factorise the RHS to get

thus the three roots are

and I haven't got a clue where you got

Edit: I haven't actually done all of that, I have given the method but worked back from your answers from the MS so it might not be all correct.

[steve2005]

-21/2 should have been written as -5/2 he meant minus 2 and a half.

[cricket001]

thanks to both steve 2005 and member910132. really appreciate the help....