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The number of integral terms in the expansion of (sqrt3 + cubicroot 5) 256 ?

The number of integral terms in the expansion of (sqrt3 + cubicroot 5)256?

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
7 years ago
Write the general term of the expression.
Tr+1=256Cr3(256-r)/25r/3

The non integral part of this term is= 3(256-r)/25r/3
Hence the value of r should be such that it gives a whole number in the power of 3 and 5.
i.e.(256-r)/2 and r/3 should give positive integral values. The values possible are
r= 0,6, 12, 18.................252
We get an AP in the values of r satisfying these conditions where a=0, d=6 and an=252.
Find the value of n to get the answer.

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