The difference between the squares of numbers is 32 Three ti

The difference between the squares of numbers is 32. Three times the square of the first number increased by the square of the second number is 112. Find the numbers The numbers are Square. (Type ordered pairs Use a comma to separate answers.)

Solution

Let the nos. be x and y

we form eqautions based on information given :

x^2 - y^2 = 32 ----(1)

3x^2 +y^2 = 112 ----(2)

add the two equations :

4x^2 = 144

x^2 = 36 ; x = -6 , 6

x^2 - y^2 =32

y^2 = x^2 -32 = 36 -32 = 4

y = -2 , 2

Solution ( -6, 2 ) , ( -6 , -2) , ( 6 , -2) , ( 6 , 2)