Final answer:
The problem involves finding two numbers whose squares' difference is -20 and whose sum is 10. By setting up a system of equations and using substitution, we find the two numbers to be 4 and 6. Thus, the correct pair is (4, 6).
Step-by-step explanation:
The problem presents a system of equations based on the properties of squares and the sum of two numbers. To solve it, we can set up the system:
- Let the two numbers be x and y.
- x² - y² = -20, which is the difference of two squares.
- x + y = 10, which is the sum of the two numbers.
We can use the factoring identity a² - b² = (a + b)(a - b) to rewrite the first equation as (x + y)(x - y) = -20.
Since we know that x + y = 10, we can substitute this into our identity to get 10(x - y) = -20. Dividing both sides by 10 gives us x - y = -2. Now we have the system:
Adding these two equations, we get 2x = 8, so x = 4. Substituting x = 4 into x + y = 10, we find that y = 6. Therefore, the two numbers are 4 and 6.
Given options are (4,-6), (-4,6), (-4,-6), (4,6). Only one pair, (4, 6), satisfies the conditions of the problem.