While minimizing two variable $$\min_{s\in\mathbb{R},x\in\mathbb{R^n}} \sqrt{x^TAx}-s $$ $$ subject\ to \ x^Te=1\ and \ x^Tu = s$$ A: n × n symmetric positive definite matrix
e: the n-vector of ones
μ: a given n-vector
Initially I fixed s and solved function with Lagrange multipliers to include constraints and get some value for x( $x^*(s)$). For the next step I replaced x with the value I found but I am not sure about including the $x^Tu=s$ constraint and solve it by Lagrangian method or should I just not include any constraint and directly use fermat theorem to find a minimum value for s.