Final answer:
After calculation, it was determined that no option among a) 4 and 6, b) 3 and 7, c) 5 and 5, and d) 2 and 8 splits the number 10 into two parts with the difference between their squares being 60; hence, there is no correct solution within the given options.
Step-by-step explanation:
We are asked to split the number 10 into two parts such that the difference between the squares of these parts equals 60. Let's denote these two parts as x and 10 - x. The equation we are looking to solve is (x^2) - (10 - x)^2 = 60.
Expanding and simplifying the equation gives us:
- x^2 - (100 - 20x + x^2) = 60
- 2x^2 - 20x - 60 = 0
- x^2 - 10x - 30 = 0
- (x-15)(x+2) = 0
The values that satisfy the equation are x = 15 and x = -2. However, since we are looking for a part of the number 10, x needs to be between 0 and 10, so the only possible solution is x = 15 with the other part being -5 (which is outside of the range). This indicates that there is no solution that splits the number 10 into two positive parts with the required condition; therefore, the options a) 4 and 6, b) 3 and 7, c) 5 and 5, and d) 2 and 8 all do not satisfy the condition.