IIT JEE , AIEEE Forum - Mathematics , Algebra

ankitagg

the sum of all rational numbers in the expansion of (3^1/5+4^1/5)^15 is

(a)39
(b)59
(c)41
(d)61

sandeepramesh

answer is clearly none of these if you consider the fact that (4^1/5)^15 + (3^1/5)^15 = 4^3 + 3^3 = 91 in itself :)

dream_iit

^^^^^^

are u sure u r correct?

Conjurer

Ankit dude you have mistyped the question LOL.Should have asked in class na, its so simple. xD

Question had 2^1/3 and not 4^1/5

or something like that dont really remember

ankitagg

sorry friends, i have typed wrong .the question is the sum of all rational numbers in the expansion of (3^1/5+2^1/3)^15 is

uday_zingtudor

You get rational nos only when in the expansion both (3^1/5)^x(2^1/3)^y is rational where x+y=15

Now this happens when x and y both are factors of 15 and when x or y =0 and 15

when x=5 it can rationalize the first part but y being 10 can rationalize the second part

x=10 can rationalize first one but again y=5 can't rationalise 2^1/3

x=15 implies y=0 . Now u get one term as 3^3=27

trying to rationalize 2^1/3 you can again observe that the first part again doiesn't get rationalized

x=o and y=15 implies another term 2^5=32

The simple reason is that the lcm of 3 and 5 is 15 and there would no factor for it in the middle of the expansion of index 15.

So the answer is 59
.
~Cheerio!!!

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