64/8*x^12=8/x^12

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Solution for 64/8*x^12=8/x^12 equation: 


D( x )

x^12 = 0

x^12 = 0

x^12 = 0

1*x^12 = 0 // : 1

x^12 = 0

x = 0

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

(64/8)*x^12 = 8/(x^12) // - 8/(x^12)

(64/8)*x^12-(8/(x^12)) = 0

(64/8)*x^12-8*x^-12 = 0

8*x^12-8*x^-12 = 0

t_1 = x^12

8*t_1^1-8*t_1^-1 = 0

8*t_1^1-8*t_1^-1 = 0

(8*t_1^2-8*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(8*t_1^2-8*t_1^0) = 0

t_1^1

8*t_1^2-8 = 0

8*t_1^2-8 = 0

DELTA = 0^2-(-8*4*8)

DELTA = 256

DELTA > 0

t_1 = (256^(1/2)+0)/(2*8) or t_1 = (0-256^(1/2))/(2*8)

t_1 = 1 or t_1 = -1

t_1 in { -1, 1} 

t_1 = -1

x^12+1 = 0

1*x^12 = -1 // : 1

x^12 = -1

t_1 = 1

x^12-1 = 0

1*x^12 = 1 // : 1

x^12 = 1

x^12 = 1 // ^ 1/12

abs(x) = 1

x = 1 or x = -1

x in { 1, -1 }

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