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Popular Word Problems >

The difference between the squares of two numbers is 15. Three times the square of the first number increased by the square of the second number is 49. 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 15. T h ree t im es 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 49. F in d t h e n u mb ers .

Solution

The numbers : 4, 1 or 4, - 1 or - 4, 1 or - 4, - 1

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x^{2} - y^{2} = 15

3 x^{2} + y^{2} = 49

Solve the system of equations:

x^{2} - y^{2} = 15, 3 x^{2} + y^{2} = 49 : x = 4, x = 4, x = - 4, x = - 4, y = 1 y = - 1 y = 1 y = - 1

The numbers : 4, 1 or 4, - 1 or - 4, 1 or - 4, - 1

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