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The difference between the squares of two numbers is 24. Four times the square of the first number increased by the square of the second number is 101. Find the numbers.

Solution

Solution

The numbers : 5, 1 or 5, - 1 or - 5, 1 or - 5, - 1

Solution steps

Represent the numbers with

x and y

number 1 : x

number 2 : y

A.T.Q.:

x^{2} - y^{2} = 24

4 x^{2} + y^{2} = 101

Solve the system of equations:

x^{2} - y^{2} = 24, 4 x^{2} + y^{2} = 101 : x = 5, x = 5, x = - 5, x = - 5, y = 1 y = - 1 y = 1 y = - 1

The numbers : 5, 1 or 5, - 1 or - 5, 1 or - 5, - 1

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