1/k=x^2-x+1

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Solution for 1/k=x^2-x+1 equation: 


x in (-oo:+oo)

1/k = x^2-x+1 // - x^2-x+1

1/k-x^2+x-1 = 0

k^-1-x^2+x-1 = 0

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

DELTA = 4*(k^-1-1)+1

4*(k^-1-1)+1 = 0

4*(k^-1-1)+1 = 0

4*k^-1-3 = 0

4*k^-1-3 = 0

4*k^-1 = 3 // : 4

k^-1 = 3/4

-1 < 0

1/(k^1) = 3/4 // * k^1

1 = 3/4*k^1 // : 3/4

4/3 = k^1

k = 4/3

DELTA = 0  <=>  t_1 = 4/3

x = -1/(-1*2) i k = 4/3

x = 1/2 i k = 4/3

( x = ((4*(k^-1-1)+1)^(1/2)-1)/(-1*2) or x = (-(4*(k^-1-1)+1)^(1/2)-1)/(-1*2) ) i k > 4/3

( x = ((4*(k^-1-1)+1)^(1/2)-1)/(-2) or x = ((4*(k^-1-1)+1)^(1/2)+1)/2 ) i k > 4/3

k-4/3 > 0

k-4/3 > 0 // + 4/3

k > 4/3

x in { 1/2, ((4*(k^-1-1)+1)^(1/2)-1)/(-2), ((4*(k^-1-1)+1)^(1/2)+1)/2 }

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