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The difference between two positive integers is 4. The sum of the larger and the square of the smaller is 34. Find the integers.

Solution

The difference between two positive integers is 4. The sum of the larger and the square of the smaller is 34. Find the integers.

Solution

The numbers : 9, 5

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x - y = 4

x + y^{2} = 34

Solve the system of equations:

x - y = 4, x + y^{2} = 34 : (x = - 2, x = 9, y = - 6 y = 5)

Select positive solutions:

5, 9

The numbers : 9, 5

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