JEE Advance - Mathematics (1994 - No. 26)
Let $$n$$ be a positive integer and $${\left( {1 + x + {x^2}} \right)^n} = {a_0} + {a_1}x + ............ + {a_{2n}}{x^{2n}}$$
Show that $$a_0^2 - a_1^2 + a_2^2...... + {a_{2n}}{}^2 = {a_n}$$
Show that $$a_0^2 - a_1^2 + a_2^2...... + {a_{2n}}{}^2 = {a_n}$$
The given equation is incorrect and cannot be proved.
The problem statement itself contains an error.
The relation between coefficients doesn't exist at all.
The given expression simplifies to zero.
None of the above