(48x^6-32x^4-40x^2)/(-8x^2)

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Solution for (48x^6-32x^4-40x^2)/(-8x^2) equation:


D( x )

-8*x^2 = 0

-8*x^2 = 0

-8*x^2 = 0

-8*x^2 = 0 // : -8

x^2 = 0

x = 0

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

(48*x^6-(32*x^4)-(40*x^2))/(-8*x^2) = 0

(48*x^6-32*x^4-40*x^2)/(-8*x^2) = 0

(48*x^6-(32*x^4)-(40*x^2))/(-8*x^2) = 0 // * -8*x^2

48*x^6-(32*x^4)-(40*x^2) = 0

48*x^6-32*x^4-40*x^2 = 0

t_1 = x^2

48*t_1^3-32*t_1^2-40*t_1^1 = 0

48*t_1^3-32*t_1^2-40*t_1 = 0

8*t_1*(6*t_1^2-4*t_1-5) = 0

6*t_1^2-4*t_1-5 = 0

DELTA = (-4)^2-(-5*4*6)

DELTA = 136

DELTA > 0

t_1 = (136^(1/2)+4)/(2*6) or t_1 = (4-136^(1/2))/(2*6)

t_1 = (2*34^(1/2)+4)/12 or t_1 = (4-2*34^(1/2))/12

8*t_1 = 0

8*t_1 = 0 // : 8

t_1 = 0

t_1 = (4-2*34^(1/2))/12

x^2-((4-2*34^(1/2))/12) = 0

1*x^2 = (4-2*34^(1/2))/12 // : 1

x^2 = (4-2*34^(1/2))/12

t_1 = (2*34^(1/2)+4)/12

x^2-((2*34^(1/2)+4)/12) = 0

1*x^2 = (2*34^(1/2)+4)/12 // : 1

x^2 = (2*34^(1/2)+4)/12

x^2 = (2*34^(1/2)+4)/12 // ^ 1/2

abs(x) = ((2*34^(1/2)+4)^(1/2))/(2*3^(1/2))

x = ((2*34^(1/2)+4)^(1/2))/(2*3^(1/2)) or x = -(((2*34^(1/2)+4)^(1/2))/(2*3^(1/2)))

t_1 = 0

x^2+0 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 0}

x in { ((2*34^(1/2)+4)^(1/2))/(2*3^(1/2)), -(((2*34^(1/2)+4)^(1/2))/(2*3^(1/2))) }

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