5-1/k-1/k^2=0

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Solution for 5-1/k-1/k^2=0 equation: 


D( k )

k^2 = 0

k = 0

k^2 = 0

k^2 = 0

1*k^2 = 0 // : 1

k^2 = 0

k = 0

k = 0

k = 0

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

5-(1/k)-(1/(k^2)) = 0

5-k^-1-k^-2 = 0

t_1 = k^-1

5-1*t_1^2-1*t_1^1 = 0

5-t_1^2-t_1 = 0

DELTA = (-1)^2-(-1*4*5)

DELTA = 21

DELTA > 0

t_1 = (21^(1/2)+1)/(-1*2) or t_1 = (1-21^(1/2))/(-1*2)

t_1 = (21^(1/2)+1)/(-2) or t_1 = (1-21^(1/2))/(-2)

t_1 = (21^(1/2)+1)/(-2)

k^-1-((21^(1/2)+1)/(-2)) = 0

1*k^-1 = (21^(1/2)+1)/(-2) // : 1

k^-1 = (21^(1/2)+1)/(-2)

-1 < 0

1/(k^1) = (21^(1/2)+1)/(-2) // * k^1

1 = ((21^(1/2)+1)/(-2))*k^1 // : (21^(1/2)+1)/(-2)

-2*(21^(1/2)+1)^-1 = k^1

k = -2*(21^(1/2)+1)^-1

t_1 = (1-21^(1/2))/(-2)

k^-1-((1-21^(1/2))/(-2)) = 0

1*k^-1 = (1-21^(1/2))/(-2) // : 1

k^-1 = (1-21^(1/2))/(-2)

-1 < 0

1/(k^1) = (1-21^(1/2))/(-2) // * k^1

1 = ((1-21^(1/2))/(-2))*k^1 // : (1-21^(1/2))/(-2)

-2*(1-21^(1/2))^-1 = k^1

k = -2*(1-21^(1/2))^-1

k in { -2*(21^(1/2)+1)^-1, -2*(1-21^(1/2))^-1 }

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