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The difference between the two numbers is 5, and the difference between their squares is 65. The numbers are ______?

The difference between the two numbers is 5, and the difference between their squares is 65. The numbers are ______?

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