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Popular Word Problems >

The difference between the squares of two numbers is 5 . Twice the square of the first number increased by the square of the second number is 22 . Find the numbers

Solution

T h e d i ff ere n ce b e tw ee n t h e s q u a res o f tw o n u mb ers i s 5 . Tw i ce t h e s q u a re o f t h e f i rs t n u mb er in cre a se d b y t h e s q u a re o f t h e seco n d n u mb er i s 22 . F in d t h e n u mb ers

Solution

The numbers : 3, 2 or 3, - 2 or - 3, 2 or - 3, - 2

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x^{2} - y^{2} = 5

2 x^{2} + y^{2} = 22

Solve the system of equations:

x^{2} - y^{2} = 5, 2 x^{2} + y^{2} = 22 : x = 3, x = 3, x = - 3, x = - 3, y = 2 y = - 2 y = 2 y = - 2

The numbers : 3, 2 or 3, - 2 or - 3, 2 or - 3, - 2

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