Réponse:
Let's denote the two numbers as x and y. We know that the difference between them is 5, so we have the equation:
x - y = 5 (1)
We also know that the sum of their squares is 73, so we have:
x^2 + y^2 = 73 (2)
From equation (1), we can express x as y + 5 and substitute it into equation (2):
(y + 5)^2 + y^2 = 73
Expanding the left side:
y^2 + 10y + 25 + y^2 = 73
Combining like terms:
2y^2 + 10y + 25 = 73
Subtracting 73 from both sides:
2y^2 + 10y - 48 = 0
Dividing by 2 to simplify:
y^2 + 5y - 24 = 0
Now, we can factor the quadratic equation:
(y + 8)(y - 3) = 0
Setting each factor to zero gives us the possible values for y:
y + 8 = 0 -> y = -8
y - 3 = 0 -> y = 3
Since the difference between the two numbers is 5, y must be 3. Therefore, the two numbers are 3 and 8.
