Asked by | 29th Dec, 2009, 06:44: PM
Consider (x+y)n general term = nCr Xn-r Y r
( (7)^1/2 + (5)^1/6 )^78 in this case general term =78Cr 7 (78-r)/2 5r/6
To get integer terms (78-r)/2 and r/6 must be integers.
Consider (78-r)/2 will be integer if and only if r is even , so allowed r values are 0, 2,4 ......78.
r/6 will be integer if and only if r is a multiple of 6, so allowed r values are 0,6 , 12, ...78.
See the common values of r in above to series of values.
So there will be 14 intigral terms .
Simple way to find solution is lake LCM of 2 and 6 . Devide the 78 by that LCM and add 1 to the answer ( 0 th term)
Answered by | 31st Dec, 2009, 08:48: AM
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