System_of_Equations_Calculation.py

import numpy as np
import sympy as sp

x, y = sp.symbols('x y')

# Define the equations
equation1 = 4**(sp.sqrt(x**2 - y**2)) + 4**(sp.sqrt(x**2 + y**2)) - 32
equation2 = sp.log(x - y, 3) + sp.log(x + y, 3) - 1

# Solve the system of equations
solutions = sp.solve((equation1, equation2), (x, y))

# Print the solutions
print("Solutions:")
for solution in solutions:
    x_val, y_val = solution
    print(f"x = {x_val}, y = {y_val}")


# Answer: Solutions:
#         x = -sqrt(24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2)), y = -sqrt(-24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2))
#         x = -sqrt(24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2)), y = sqrt(-24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2))
#         x = sqrt(24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2)), y = -sqrt(-24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2))
#         x = sqrt(24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2)), y = sqrt(-24*log(2)**2 + 2*(log(32 - 4**(sqrt(3))) + 2*I*pi)**2)/(4*log(2))
#         x = sqrt(24*log(2)**2 + 2*log(32 - 4**(sqrt(3)))**2)/(4*log(2)), y = -sqrt(-24*log(2)**2 + 2*log(32 - 4**(sqrt(3)))**2)/(4*log(2))
#         x = sqrt(24*log(2)**2 + 2*log(32 - 4**(sqrt(3)))**2)/(4*log(2)), y = sqrt(-24*log(2)**2 + 2*log(32 - 4**(sqrt(3)))**2)/(4*log(2))