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If ((a+b)^n - (2^n - 3^n)) is divisible by ab, then find (a-b)^2...pls help with atleast one step..it will do..thanks..

If ((a+b)^n - (2^n - 3^n)) is divisible by ab, then find (a-b)^2...pls help with atleast one step..it will do..thanks..

Grade:12

1 Answers

Aditya Gupta
2081 Points
3 years ago
using binomial theorem we get
(a+b)^n= a^n + b^n + ab*k (where k is an integer assuming a and b are integers, we have simply taken ab common from remaining terms)
now i think it should be (a+b)^n - (2^n + 3^n) bcoz then we can write it as a^n + b^n + ab*k – (2^n + 3^n) 
= (a^n – 2^n) + (b^n – 3^n) + abk or (b^n – 2^n) + (a^n – 3^n) + abk.
now if (a,b)= (2, 3) or (3, 2) then clearly the term is divisible by ab. in both cases (a – b)^2= 1.
so just check the ques once again and let me know if you r still facing any issue...
KINDLY APPROVE :))

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