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

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Solution for (2x-(1/x))^2 equation:


D( x )

x = 0

x = 0

x = 0

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

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

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

2*x-x^-1 = 0

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

2*x^2 = 1 // : 2

x^2 = 1/2

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

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

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

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

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

( x+(1/2)^(1/2) )

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

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

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

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

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

( x^-1 )

1*x^-1 = 0 // : 1

x^-1 = 0

x należy do O

x in { -(1/2)^(1/2), -(1/2)^(1/2), (1/2)^(1/2), (1/2)^(1/2) }

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