7x^2-1/x^2

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Solution for 7x^2-1/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

7*x^2-(1/(x^2)) = 0

7*x^2-x^-2 = 0

t_1 = x^2

7*t_1^1-1*t_1^-1 = 0

7*t_1^1-1*t_1^-1 = 0

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

t_1^1*(7*t_1^2-1*t_1^0) = 0

t_1^1

7*t_1^2-1 = 0

7*t_1^2-1 = 0

DELTA = 0^2-(-1*4*7)

DELTA = 28

DELTA > 0

t_1 = (28^(1/2)+0)/(2*7) or t_1 = (0-28^(1/2))/(2*7)

t_1 = (1*7^(1/2))/7 or t_1 = (-7^(1/2))/7

t_1 in { (-7^(1/2))/7, (1*7^(1/2))/7} 

t_1 = (-7^(1/2))/7

x^2-((-7^(1/2))/7) = 0

1*x^2 = (-7^(1/2))/7 // : 1

x^2 = (-7^(1/2))/7

t_1 = (1*7^(1/2))/7

x^2-((1*7^(1/2))/7) = 0

x^2-((7^(1/2))/7) = 0

1*x^2 = (7^(1/2))/7 // : 1

x^2 = (7^(1/2))/7

x^2 = (7^(1/2))/7 // ^ 1/2

abs(x) = 7^(-1/4)

x = 7^(-1/4) or x = -7^(-1/4)

x in { 7^(-1/4), -7^(-1/4) }

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