# Misc 2 - Chapter 8 Class 11 Binomial Theorem

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 2 Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal. We know that General term of expansion (a + b)n is Tr+1 = nCr (a)n–r . br For (3 + ax)9 , Putting a = 3 , b = 9x & n = 9 General term of (3 + ax )9 is Tr+1 = 9Cr (3)9–r . (ax)r = 9Cr 39–r . ar . xr We need Coefficient of x2 & x3 Given that Coefficient of x2 = coefficient of x3 9C2 (3)7 . a2 = 9C2 (3)6 . a3 9!2!9 −2! 37 . a2 = 9!3!9 −3! 36 . a3 9!2!7! 37 . a2 = 9!3!6! 36 . a3 9!2! 7! . 379!3!9 −3! . 36 = 𝑎3𝑎2 9!2! 7! . 37 × 3! 6!9! . 36 = a 9! × 3! × 6!9! × 2! × 7! × 3736 = a 3 ×2! ×6!2! ×7 ×6! . 3 = a 37 × 3 = a 97 = a Hence, a = 97

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.