SOLUTION: If a term in the explansion of (x+b)^8 is (-1701x^3)/(4096), assuming b is a constant, then the exact value of b is?

Algebra ->  Permutations -> SOLUTION: If a term in the explansion of (x+b)^8 is (-1701x^3)/(4096), assuming b is a constant, then the exact value of b is?      Log On


   



Question 386772: If a term in the explansion of (x+b)^8 is (-1701x^3)/(4096), assuming b is a constant, then the exact value of b is?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The binomial theorem states that, the (r+1)st term in the expansion of %28a+%2B+b%29%5En is nCr%2Aa%5E%28n-r%29%2Ab%5Er. Applied directly to the problem at hand, knowing that the power of x should be 3, the term involving x%5E3 should then be 8C5%2Ax%5E3%2Ab%5E5. Thus
8C5+%2A+b%5E5+=+-1701%2F4096, after equating coefficients. Then
56b%5E5+=+-1701%2F4096, or
b%5E5+=+-243%2F32768, or
b+=+-3%2F8.