(x^-2)-((x^2)/16)

Solution for (x^-2)-((x^2)/16) equation:

D( x )

x = 0

x = 0

x = 0

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

x^-2-((x^2)/16) = 0

x^-2-1/16*x^2 = 0

t_1 = x^2

1*t_1^-1-1/16*t_1^1 = 0

1*t_1^-1-1/16*t_1^1 = 0

(1*t_1^0-1/16*t_1^2)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^0-1/16*t_1^2) = 0

t_1^1

(-1/16)*t_1^2+1 = 0

(-1/16)*t_1^2+1 = 0

DELTA = 0^2-(1*4*(-1/16))

DELTA = 1/4

DELTA > 0

t_1 = ((1/4)^(1/2)+0)/(2*(-1/16)) or t_1 = (0-(1/4)^(1/2))/(2*(-1/16))

t_1 = -4 or t_1 = 4

t_1 in { -4, 4} 

t_1 = -4

x^2+4 = 0

1*x^2 = -4 // : 1

x^2 = -4

t_1 = 4

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in { 2, -2 }