Here in $${\left( {\sqrt 3 } \right)^{2n - 1}}$$, 2n - 1 is odd number. So there will be always $${\sqrt 3 }$$ in $${\left( {\sqrt 3 } \right)^{2n - 1}}$$.
So $${\left( {\sqrt 3 + 1} \right)^{2n}} - {\left( {\sqrt 3 - 1} \right)^{2n}}$$ will be always irrational number.
2
AIEEE 2011
MCQ (Single Correct Answer)
The coefficient of $${x^7}$$ in the expansion of $${\left( {1 - x - {x^2} + {x^3}} \right)^6}$$ is
A
$$-132$$
B
$$-144$$
C
$$132$$
D
$$144$$
Explanation
Given,
$${\left( {1 - x - {x^2} + {x^3}} \right)^6}$$