2407.sagews

X, n, V = var('X, n, V')

def b(X, n, V):
    r = V / (1 - V) * X / (1+X)
    return r

def ev(X, n, V):
    r = b(X, n, V)* (1 - n) - n * X

diff(b(X, n, V) - n * X, X)

-n - V/((X + 1)*(V - 1)) + V*X/((X + 1)^2*(V - 1))

solve([-n - V/((X + 1)*(V - 1)) + V*X/((X + 1)^2*(V - 1)) == 0], X)

[X == -(V*n - n + sqrt(-V^2*n + V*n))/(V*n - n), X == -(V*n - n - sqrt(-V^2*n + V*n))/(V*n - n)]