(2a-1/a)^2

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


D( a )

a = 0

a = 0

a = 0

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

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

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

2*a-a^-1 = 0

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

2*a^2 = 1 // : 2

a^2 = 1/2

a^2 = 1/2 // ^ 1/2

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

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

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

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

( a+(1/2)^(1/2) )

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

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

( a-(1/2)^(1/2) )

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

a = (1/2)^(1/2)

( a^-1 )

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

a^-1 = 0

a należy do O

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

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