The difference between the two numbers is 5, and the difference between their squares is 65. The numbers are ______?
Answer: 9 and 4
Explanation
Let's directly calculate:
x - y = 5
x² - y² = 65
(x + y)(x - y) = 65
(x + y)(5) = 65
x + y = 13
Solving these equations:
x - y = 5
x + y = 13
Adding both: 2x = 18
x = 9
y = 4
Let's check:
9 - 4 = 5
9² - 4² = 81 - 16 = 65
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