
#1
Feb1012, 08:05 AM

P: 2

1. The problem statement, all variables and given/known data
I'm asked to find (a/b) in the simplest form if the coefficient of x^8 is zero in the expansion of: (1 + x)(a  bx)^12 2. Relevant equations Binomial expansion formula ... (a + b)^n = Sum of r > n (r = 0) (nCr)(a^(nr) * b^r 3. The attempt at a solution I figured that x^8 could be achieved from two possible situations ... either 1 * the expansion of (a  bx)^12 or x * the expansion of (a  bx)^12 I found the value of r at both these points by looking for the value of r that makes bx^r = x^8 and x*bx^r = x^8. This I found to be r = 7 and r = 8. Then I wrote as: (12C7) * (a)^5 * (b)^7 + (12C7) * (a)^4 * (b)^8 = 0 Then I get stuck as I cannot seem to get values for a and b from this. Can anyone help me? 



#2
Feb1012, 09:38 AM

P: 2

Problem solved ...
First of all, note my error in the last line (12C7) * (a)^5 * (b)^7 + (12C7) * (a)^4 * (b)^8 = 0 Should be: (12C7) * (a)^5 * (b)^7 + (12C8) * (a)^4 * (b)^8 = 0 The negative b on the (b)^7 comes out the front as it is an odd power ... The other negative cancels out (12C7) * (a)^5 * (b)^7 + (12C8) * (a)^4 * (b)^8 = 0 throw the negative section over to the other side of the equals sign ... (12C8) * (a)^4 * (b)^8 = (12C7) * (a)^5 * (b)^7 then evaluate => (495)*(a^4)*(b^8) = (792)*(a^5)*(b^7) start cancelling => (495)*(b) = (792)*(a) divide to each side => 495/792 = a/b => a/b = 5/8 which is correct according to the answers. 


Register to reply 
Related Discussions  
Finding Joules of heat for 75% efficient motor at 250hp.  Introductory Physics Homework  4  
Binomial series vs Binomial theorem, scratching my head for three days on this  Calculus  6  
Finding a term in a binomial expnasion  Calculus & Beyond Homework  2  
finding resistance and temp coefficient  Engineering, Comp Sci, & Technology Homework  2  
Gravity Ratios using pronumerals  Introductory Physics Homework  2 