Question

The no. of irrational terms in the expansion of (5^1/8 + 2^1/6)^100

Answer 1

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Here Total no.of the terms in the expansion of

(5^ 1/6 + 2^ 1/8)^100 is 101.

We get rational terms in the expansion only if the powers of 5^ 1/6 and 2^ 1/8 are the multiples of 6 and 8 respectively.

Therefore These terms are nC84(5^ 1/6)^84.(2^1/8)^16,

nC60(5^ 1/6)^60.(2^ 1/8)^40.

nC36(5^ 1/6)^36. (2^ 1/8)^64 and

nC12 (5^ 1/6)^12.(5^ 1/8)^88. So 4 terms are rational and the remaining 97 terms are irrational terms.




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