1/x^2=17/4-x^2

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Solution for 1/x^2=17/4-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)

1/(x^2) = 17/4-x^2 // - 17/4-x^2

x^2+1/(x^2)-(17/4) = 0

x^2+1/(x^2)-17/4 = 0

x^2+x^-2-17/4 = 0

t_1 = x^2

1*t_1^1+1*t_1^-1-17/4 = 0

1*t_1^1+1*t_1^-1-17/4*t_1^0 = 0

(1*t_1^2-17/4*t_1^1+1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-17/4*t_1^1+1*t_1^0) = 0

t_1^1

t_1^2+(-17/4)*t_1+1 = 0

t_1^2+(-17/4)*t_1+1 = 0

DELTA = (-17/4)^2-(1*1*4)

DELTA = 225/16

DELTA > 0

t_1 = ((225/16)^(1/2)-(-17/4))/(1*2) or t_1 = (-(-17/4)-(225/16)^(1/2))/(1*2)

t_1 = 4 or t_1 = 1/4

t_1 in { 1/4, 4} 

t_1 = 1/4

x^2-1/4 = 0

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

x^2 = 1/4

x^2 = 1/4 // ^ 1/2

abs(x) = 1/2

x = 1/2 or x = -1/2

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 { 1/2, -1/2, 2, -2 }

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