Sum of Binomial Coefficients of Odd Numbered Terms
If n is a pos...
Question
If n is a positive integer, then (√3+1)2n−(√3−1)2n is :
A
an irrational number
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B
an odd positive interger
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C
an even positive interger
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D
a rational number other than positive integers
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Solution
The correct option is A an irrational number (√3+1)2n−(√3−1)2n=[(√3+1)2]n−[(√3−1)2]n=(4+2√3)n−(4−2√3)n=2n[(2+√3)n−(2−√3)n]=2n×2[nC12n−1√3+nC3.2n−33√3+...]=2n+1√3[nC12n−1+nC32n−33+....] =√3×Some integer ∴ irrational number