4v^2-16/v^2-2

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Solution for 4v^2-16/v^2-2 equation: 


D( v )

v^2 = 0

v^2 = 0

v^2 = 0

1*v^2 = 0 // : 1

v^2 = 0

v = 0

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

4*v^2-(16/(v^2))-2 = 0

4*v^2-16*v^-2-2 = 0

t_1 = v^2

4*t_1^1-16*t_1^-1-2 = 0

4*t_1^1-16*t_1^-1-2*t_1^0 = 0

(4*t_1^2-2*t_1^1-16*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(4*t_1^2-2*t_1^1-16*t_1^0) = 0

t_1^1

4*t_1^2-2*t_1-16 = 0

4*t_1^2-2*t_1-16 = 0

DELTA = (-2)^2-(-16*4*4)

DELTA = 260

DELTA > 0

t_1 = (260^(1/2)+2)/(2*4) or t_1 = (2-260^(1/2))/(2*4)

t_1 = (2*65^(1/2)+2)/8 or t_1 = (2-2*65^(1/2))/8

t_1 in { (2-2*65^(1/2))/8, (2*65^(1/2)+2)/8} 

t_1 = (2-2*65^(1/2))/8

v^2-((2-2*65^(1/2))/8) = 0

1*v^2 = (2-2*65^(1/2))/8 // : 1

v^2 = (2-2*65^(1/2))/8

t_1 = (2*65^(1/2)+2)/8

v^2-((2*65^(1/2)+2)/8) = 0

1*v^2 = (2*65^(1/2)+2)/8 // : 1

v^2 = (2*65^(1/2)+2)/8

v^2 = (2*65^(1/2)+2)/8 // ^ 1/2

abs(v) = ((2*65^(1/2)+2)^(1/2))/(2*2^(1/2))

v = ((2*65^(1/2)+2)^(1/2))/(2*2^(1/2)) or v = -(((2*65^(1/2)+2)^(1/2))/(2*2^(1/2)))

v in { ((2*65^(1/2)+2)^(1/2))/(2*2^(1/2)), -(((2*65^(1/2)+2)^(1/2))/(2*2^(1/2))) }

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