Solve the following equation x2 y2 8 x2 y 2Solutionx2 y

Solve the following equation

x^2 + y^2 = 8

x^2 - y = 2

x^2 + y^2 = 8 ---(1)

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

y = x^2 - 2

substitute in equation 1:

x^2 + (x^2 -2)^2 = 8

x^2 + x^4 +4 -4x^2 =8

x^4 - 3x^2 -4 =0

x^4 -4x^2 +x^2 -4 =0

x^2(x^2 -4) + 1( x^2 -4) =0

(x^2 +1)(x^2 -4) =0

x= i, -i ; x = -2 , 2

find y : x^2 -y = 2

y = x^2 -2 = 1 -2 = -1

y = 4 -2 = 2

Solution : (x , y) = ( -i, -1) ( i, -1) ( -2 , 2) and ( 2 , 2)