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the sum of two positive numbers is 7 times their difference. the difference of the squares of these numbers is twice the sum of the numbers. find these numbers

Solution

Solution

The numbers : 8, 6

Solution steps

Represent the numbers with

x and y

number 1 : x

number 2 : y

A.T.Q.:

x + y = 7 (x - y)

x^{2} - y^{2} = 2 (x + y)

Solve the system of equations:

x + y = 7 (x - y), x^{2} - y^{2} = 2 (x + y) : (x = 8, x = 0, y = 6 y = 0)

Select positive solutions:

6, 8

The numbers : 8, 6

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