Question 1151211
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            I will show you how to solve this problem quickly and mentally.


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From the condition, you have this system of 2 equations

    x - y = 3              (1)

    x^2 + y^2 = 45.        (2)


Square equation (1); keep equation (2) as is.

    x^2 - 2x + y^2 = 9     (1')

    x^2      + y^2 = 45    (2')


Now subtract equation (1') from equation (1'). You will get


         2xy       = 45 - 9 = 36,   or

          xy                = 36/2 = 18.


Thus you have two numbers x and y  with the difference of 3 and the product of 18.


3 seconds is enough to guess (to recognize) these numbers,  3 and 6.
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Solved.