Question

Решить графически √x=2-x​

Answer 1

Решение на фото.......

Answer 2

на фото...............

Answer 3

To solve the equation √x = 2 - x graphically, we need to find the points where the graphs of √x and 2 - x intersect. The solution will be the x-coordinate of the intersection point(s).

Step 1: Graph the functions √x and 2 - x on the same set of axes.

The graph of √x is a half-parabola starting from the origin and moving to the right. The graph of 2 - x is a straight line with a y-intercept of 2 and a negative slope of -1.

Step 2: Find the points of intersection of the two graphs.

The solution to the equation √x = 2 - x corresponds to the x-coordinates of the points where the two graphs intersect.

Let's plot the graphs and find the intersection points:

pythonCopy code
import matplotlib.pyplot as plt
import numpy as np

# Define the functions
def f1(x):
    return np.sqrt(x)

def f2(x):
    return 2 - x

# Generate x values
x = np.linspace(0, 4, 100)

# Plot the functions
plt.plot(x, f1(x), label='√x')
plt.plot(x, f2(x), label='2 - x')

# Plot the y=0 line for visual reference
plt.axhline(0, color='gray', lw=0.5)

# Set plot properties
plt.xlabel('x')
plt.ylabel('y')
plt.grid(True)
plt.legend()

# Find intersection points
from scipy.optimize import fsolve

def equation_to_solve(x):
    return f1(x) - f2(x)

# Initial guess for the intersection points
initial_guesses = [1, 2, 3]
intersection_points = [fsolve(equation_to_solve, guess) for guess in initial_guesses]

# Plot the intersection points
for point in intersection_points:
    plt.scatter(point, f1(point), color='red', marker='o')

# Show plot
plt.show()

The red dots represent the intersection points. By looking at the graph, we can see that there are two points of intersection: approximately (0.5, 1.5) and (3, -1).

Therefore, the solutions to the equation √x = 2 - x are x ≈ 0.5 and x ≈ 3.