y^2+256/y^2=32

Solution for y^2+256/y^2=32 equation:

D( y )

y^2 = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

y in (-oo:0) U (0:+oo)

y^2+256/(y^2) = 32 // - 32

y^2+256/(y^2)-32 = 0

y^2+256*y^-2-32 = 0

t_1 = y^2

1*t_1^1+256*t_1^-1-32 = 0

1*t_1^1+256*t_1^-1-32*t_1^0 = 0

(1*t_1^2-32*t_1^1+256*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-32*t_1^1+256*t_1^0) = 0

t_1^1

t_1^2-32*t_1+256 = 0

t_1^2-32*t_1+256 = 0

DELTA = (-32)^2-(1*4*256)

DELTA = 0

t_1 = 32/(1*2)

t_1 = 16 or t_1 = 16

t_1 in { 16, 16} 

t_1 = 16

y^2-16 = 0

1*y^2 = 16 // : 1

y^2 = 16

y^2 = 16 // ^ 1/2

abs(y) = 4

y = 4 or y = -4

t_1 = 16

y^2-16 = 0

1*y^2 = 16 // : 1

y^2 = 16

y^2 = 16 // ^ 1/2

abs(y) = 4

y = 4 or y = -4

y in { 4, -4, 4, -4 }