JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 22

Let the mean and the variance of 20 observations $x_1,x_2,\dots,x_{20}$ be 15 and 9, respectively. For α ∈ R, if the mean of $(x_1+\alpha)^2,(x_2+\alpha)^2,\dots,(x_{20}+\alpha)^2$ is 178, then the square of the maximum value of α is equal to _______.