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The sum of the rational terms in the binomial expansion (2^1/3+3^1/5) is.

The sum of the rational terms in the binomial expansion (2^1/3+3^1/5) is.   

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
( 3^1/5 + 2^1/3)^15 = 
15C0*(3^1/5)^15*(2^1/3)^0 + 15C1*(3^1/5)^14*(2^1/3)^1 + ....... + 15C15*(2^1/3)^15*(3^1/5)^0. 
In the first place term = 3^3 = 27. 
Second term = 15C1*3^14/5 * 2^1/3. 
3^15/4 is unreasonable . 
As rational*irrational = unreasonable, 
second term is unreasonable. 
Right off the bat, we should just consider forces of 3 . 
A similar thing will occur in the event of every single other term with the exception of (3^1/5)^10, (3^1/5)^5 and (3^1/5)^0. 
At the point when energy of 3^1/5 is 10, that of 2^1/3 is 5. In any case, 2^5/3 is nonsensical so this term, as well, is silly. 
A similar thing occurs if there should be an occurrence of (3^1/5)^5. 
At the point when energy of 3^1/5 is zero, that of 2^1/3 is 15. It's a last term. 
Last term = 2^5 = 32. 
There're just 2 reasonable terms : 27 and 32. 
Sum of reasonable terms = 59. 

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