13th pls dont send any links Q13) Find the coefficient of x7 in ax + 1bx11 and x-7 - Maths - Binomial Theorem

Question

13th pls dont send any links

Q13) Find the coefficient of x 7   in   a x   +
  1 b x 11   and   x - 7   in   a x  
- 1 b x 2 11 and find the relation between a and b so that
coefficients are equal

Neha Sethi · Accepted Answer

Dear student

We know that r+1th term in the expansion of x+an is given by:Tr+1=nCr xn-r arWe have ax+1bx11Let x7 occur in r+1th term, henceTr+1=11Crax11-r1bxr=11Cra11-rbrx11-rxr=11Cra11-rbrx11-2rAs this term contains x7⇒11-2r=7⇒4=2r⇒r=2Hence the coefficient of x7 in  ax+1bx11Coefficient of x7=11C2a11-2b2⇒Coefficient of x7=11C2a9b2ax-1bx211
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=11C6a5b6Given:Coefficient of x7 in ax+1bx11=Coefficient of x-7 in ax-1bx21111C2a9b2=11C6a5b655×a4=462b4   as nCr=n!r!n-r!a4b4=46255ab4=425ab=42514
Regards

13th. pls dont send any links Q13) Find the coefficient of x 7 in a x + 1 b x 11 and x - 7 in a x - 1 b x 2 11 and find the relation between a and b so that coefficients are equal .

13th. pls dont send any links

Q13) Find the coefficient of $x^{7} in {(a x + \frac{1}{b x})}^{11} and x^{- 7} in {(a x - \frac{1}{b x^{2}})}^{11}$ and find the relation between a and b so that coefficients are equal .