### simple numerical solve

~~Hello,
~~Hello,

Thanks for the help, I'm trying to move from Mathematica to Sage, but I'm still having some trouble with the basics. Specifically, I'm moving from 1-var to 2-var numerical optimization/solver. I want to optimize function g or, equivalently, solve ~~a fairly simple 1 variable equation, but the output ~~the system of first-order conditions, f. So far, I have not been able to get ~~is:~~

[g_a == -31375155/31496372*sqrt(-4/5*g_a + 1) +
31375155/31496372*sqrt(4/5*g_a + 8) - 35/8]

any of the scipy routines to work. Is there a simple way to ~~get a closed-form solution? Hopefully without installing a numerical optimization routine? I have not been able to get simplify to work for this.~~

Thank you!!do this?

Thanks!
jv

# Constants

y_a = 50
y_b = 50
x = 40
alpha_a = .2
alpha_b = .2

# Functions

v(n)= n^.5
v1(n) = derivative(v(n),n)
u(n)= n^.5
u1(n) = derivative(u(n),n)

# Variables

var('g_a')
var('x_a')

# Optimization

g = (v(g_a+alpha_b*(x-g_a))-u(y_a)+u(y_a-x_a))*(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))

f1 = ((1-alpha_b)*v1(g_a+alpha_b*(x - g_a)))/((1-alpha_a)*v1(x-g_a+alpha_a*(g_a)))==(v(g_a+alpha_b*(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))

f2 = (u1(x_a)/u1(x-x_a)) == (v(g_a+alpha_b*(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))

f(g_a, x_a) = (f1, f2)