Putting y = x we have,
$2f(x) + {\left[ {f(x)} \right]^2} = 1$
$2f(x) + {\left[ {f(x)} \right]^2} + 1 = 1 + 1$
${[f(x) + 1]^2} = 2$
$f(x) = - 1 \pm \sqrt 2 $
Since f(x) is a constant function, $f'(x) = 0$.
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $ $\therefore 2^n = 4096 =2^{12} $ $\Rightarrow n = 12 $ Greatest coefficient = ${}^{12}{C_6} = 924$