def solve_quadratic(a, b, c):
    # Using substitution u = 2^x
    discriminant = b**2 - 4*a*c
    u1 = (-b + discriminant**0.5) / (2*a)
    u2 = (-b - discriminant**0.5) / (2*a)
    return u1, u2

# Example: 2^(2x) - 6(2^x) + 8 = 0
# u^2 - 6u + 8 = 0 -> u=2, u=4
print(solve_quadratic(1, -6, 8))

def f(x):
    return (x**2 - 1) / (x - 2)

# Analyze behavior near x=2
# Vertical asymptote at x=2
# Oblique asymptote: y = x + 2
print("Limit as x -> 2+:", float('inf'))

import numpy as np

v1 = np.array([1, 2, 3])
v2 = np.array([4, 5, 6])

# Cross product for normal vector
normal = np.cross(v1, v2)
print("Normal vector:", normal)

from sympy import symbols, integrate, exp

x = symbols('x')
# Integrate x * e^x
result = integrate(x * exp(x), x)
print("Integral:", result)