The difference between the squares of two numbers is 3 Four

The difference between the squares of two numbers is 3. Four times the square of the fast number increased by the square of the second number is 17. Find the numbers. The numbers are. (Type ordered pairs. Use a comma to separate answers.)

Solution

Let the numbers be x and y

diff. between the squares of two numbers =3

x^2 - y^2 = 3 ----(1)

4*x^2 + y^2 = 17 ----(2)

solve the two equations :

Add the two :

5x^2 = 20 ; x^2 = 4

x = -2 , 2

substitute in equation 1 : (2^2) -y^2 = 3

y^2 = 4 -3 = 1 ; y = -1 , 1

The two numbers are ( 2, 1) , ( 2, -1) , ( -2, -1) , ( -2, 1)