x^2-1/x^2=50

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Solution for x^2-1/x^2=50 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)

x^2-(1/(x^2)) = 50 // - 50

x^2-(1/(x^2))-50 = 0

x^2-x^-2-50 = 0

t_1 = x^2

1*t_1^1-1*t_1^-1-50 = 0

1*t_1^1-1*t_1^-1-50*t_1^0 = 0

(1*t_1^2-50*t_1^1-1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-50*t_1^1-1*t_1^0) = 0

t_1^1

t_1^2-50*t_1-1 = 0

t_1^2-50*t_1-1 = 0

DELTA = (-50)^2-(-1*1*4)

DELTA = 2504

DELTA > 0

t_1 = (2504^(1/2)+50)/(1*2) or t_1 = (50-2504^(1/2))/(1*2)

t_1 = (2*626^(1/2)+50)/2 or t_1 = (50-2*626^(1/2))/2

t_1 in { (50-2*626^(1/2))/2, (2*626^(1/2)+50)/2} 

t_1 = (50-2*626^(1/2))/2

x^2-((50-2*626^(1/2))/2) = 0

1*x^2 = (50-2*626^(1/2))/2 // : 1

x^2 = (50-2*626^(1/2))/2

t_1 = (2*626^(1/2)+50)/2

x^2-((2*626^(1/2)+50)/2) = 0

1*x^2 = (2*626^(1/2)+50)/2 // : 1

x^2 = (2*626^(1/2)+50)/2

x^2 = (2*626^(1/2)+50)/2 // ^ 1/2

abs(x) = ((2*626^(1/2)+50)^(1/2))/(2^(1/2))

x = ((2*626^(1/2)+50)^(1/2))/(2^(1/2)) or x = -(((2*626^(1/2)+50)^(1/2))/(2^(1/2)))

x in { ((2*626^(1/2)+50)^(1/2))/(2^(1/2)), -(((2*626^(1/2)+50)^(1/2))/(2^(1/2))) }

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