Final answer:
The two numbers in question are -0.95 and 2.05. The smaller number was found by setting up an equation based on the given conditions and solving for x, then adding 3 to find the larger number.
Step-by-step explanation:
The student is asking to find two numbers where one is 3 more than the other and the difference between their squares is 3.3. Let's call the smaller number x and the larger number x+3. The problem can be formulated as the equation:
(x + 3)^2 - x^2 = 3.3
Expanding the left side, we get:
x^2 + 6x + 9 - x^2 = 3.3
This simplifies to:
6x + 9 = 3.3
Subtracting 9 from both sides gives:
6x = -5.7
Dividing by 6, we find:
x = -0.95
Therefore, the smaller number is -0.95 and the larger number is -0.95 + 3 = 2.05.