IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => IB => Math => Topic started by: sweet777 on November 02, 2009, 11:50:52 am

Title: binomial theorem help
Post by: sweet777 on November 02, 2009, 11:50:52 am: um how would you solve this question'?

in the expansion of (1+ax)² the first term is 1, 2nd term = 24x, 3rd term = 252x². find the value for a and n...

please tell me fast how u solve this...thanks!!!!!!!!!!!!
Title: Re: binomial theorem help
Post by: sweet777 on November 02, 2009, 03:06:24 pm: thanks for the effort...but actually, the answer at d back of the book is a = 3 and n = 8...anyways...
thanks!!
:)thank you soo much!
Title: Re: binomial theorem help
Post by: Ghost Of Highbury on November 02, 2009, 03:12:51 pm: Quote from: sweet777 on November 02, 2009, 11:50:52 am
um how would you solve this question'?

in the expansion of (1+ax)² the first term is 1, 2nd term = 24x, 3rd term = 252x². find the value for a and n...

please tell me fast how u solve this...thanks!!!!!!!!!!!!

okk...first the question u wrote is wrong..

it shud be (1+ax)ⁿ

got the answer ..will reply in my next post..plzz wait..
Title: Re: binomial theorem help
Post by: Ghost Of Highbury on November 02, 2009, 03:22:48 pm: (1+ax)ⁿ

T_r = nCr * y^n-r * z^r (y+z)ⁿ...here y=1....z = ax

ok..

y i.e 1 raised to anything willl give u 1..so we omit that..

that leaves us with

nCr * z^r

when r = 1 the coefficient is 24

so..

nC1 * ax = 24x

n * a = 24

an = 24

a = 24/n

-----------

when r = 2 the coefficient is 252

nC2 * (ax)²

nC2 * a²x² = 252x²

nC2 = (n² - n)/2

$(n^2 - n)/2 *a^2$ = 252

a = 24/n
so, a² = 576/ⁿ²

substituting this we get

$(n^2 - n)/2 *(576/n^2)$ = 252

576n² - 576n
----------------------- = 252
2n²

576n² - 576n = 504²

576n² - 504² = 576n

72n² = 576n

n = 8

substituting again in a = 24/n we get a = 3
Title: Re: binomial theorem help
Post by: IGSTUDENT on November 15, 2009, 02:40:58 am: I need help to evaluate:

(1+ sq.root 3i) raised to 3.

Please help .I have a mock coming.
Title: Re: binomial theorem help
Post by: sweet777 on November 20, 2009, 12:52:53 am: "when r = 2 the coefficient is 252

nC2 * (ax)²

nC2 * a²x² = 252x²

nC2 = (n2 - n)/2"
hey..i gt dpart in which a=24/n....but i really dont understand how you got (n² - n) from a²x²=252x²