Resposta:

Explicação passo a passo:

To solve the equation x² - 17 = 0, we can add 17 to both sides of the equation to obtain:

x² = 17

Then, we can take the square root of both sides of the equation to obtain:

x = ±√17

Therefore, the solutions to the equation x² - 17 = 0 are x = √17 and x = -√17.

To solve the equation (x+1)² = 2x - 3, we can expand the left side of the equation using the formula (a+b)² = a² + 2ab + b²:

x² + 2x + 1 = 2x - 3

Then, we can simplify the equation by subtracting 2x and adding 3 to both sides:

x² - x + 4 = 0

We can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = -1, and c = 4. Substituting these values into the quadratic formula, we obtain:

x = (1 ± √(-15)) / 2

Since the discriminant is negative, there are no real solutions to this equation. Therefore, the equation (x+1)² = 2x - 3 has no real solutions.

I hope this helps!