A real number M is squared to give the value N. What is the minimum value of (M + N)?

Given N = M². We need to minimize M + N = M + M². Let f(M) = M² + M. Taking derivative: f'(M) = 2M + 1 = 0, so M = −1/2. Then N = M² = 1/4. So M + N = −1/2 + 1/4 = −1/4 = −0.25. This is the minimum value since f''(M) = 2 > 0.