10/p2=3/p+1

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Solution for 10/p2=3/p+1 equation: 


D( p )

p = 0

p^2 = 0

p = 0

p = 0

p^2 = 0

p^2 = 0

1*p^2 = 0 // : 1

p^2 = 0

p = 0

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

10/(p^2) = 3/p+1 // - 3/p+1

10/(p^2)-(3/p)-1 = 0

10/(p^2)-3*p^-1-1 = 0

10*p^-2-3*p^-1-1 = 0

t_1 = p^-1

10*t_1^2-3*t_1^1-1 = 0

10*t_1^2-3*t_1-1 = 0

DELTA = (-3)^2-(-1*4*10)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+3)/(2*10) or t_1 = (3-49^(1/2))/(2*10)

t_1 = 1/2 or t_1 = -1/5

t_1 = -1/5

p^-1+1/5 = 0

1*p^-1 = -1/5 // : 1

p^-1 = -1/5

-1 < 0

1/(p^1) = -1/5 // * p^1

1 = -1/5*p^1 // : -1/5

-5 = p^1

p = -5

t_1 = 1/2

p^-1-1/2 = 0

1*p^-1 = 1/2 // : 1

p^-1 = 1/2

-1 < 0

1/(p^1) = 1/2 // * p^1

1 = 1/2*p^1 // : 1/2

2 = p^1

p = 2

p in { -5, 2 }

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