w2/3+w4/3=16/3

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Solution for w2/3+w4/3=16/3 equation: 


w in (-oo:+oo)

(w^4)/3+(w^2)/3 = 16/3 // - 16/3

(w^4)/3+(w^2)/3-(16/3) = 0

(w^4)/3+(w^2)/3-16/3 = 0

1/3*w^4+1/3*w^2-16/3 = 0

t_1 = w^2

1/3*t_1^2+1/3*t_1^1-16/3 = 0

1/3*t_1^2+1/3*t_1-16/3 = 0

DELTA = (1/3)^2-(-16/3*1/3*4)

DELTA = 65/9

DELTA > 0

t_1 = ((65/9)^(1/2)-1/3)/(1/3*2) or t_1 = (-(65/9)^(1/2)-1/3)/(1/3*2)

t_1 = 3/2*((65/9)^(1/2)-1/3) or t_1 = -3/2*((65/9)^(1/2)+1/3)

t_1 = -3/2*((65/9)^(1/2)+1/3)

w^2-(-3/2*((65/9)^(1/2)+1/3)) = 0

w^2+3/2*((65/9)^(1/2)+1/3) = 0

1*w^2 = -(3/2*((65/9)^(1/2)+1/3)) // : 1

w^2 = -3/2*((65/9)^(1/2)+1/3)

t_1 = 3/2*((65/9)^(1/2)-1/3)

w^2-(3/2*((65/9)^(1/2)-1/3)) = 0

w^2-3/2*((65/9)^(1/2)-1/3) = 0

1*w^2 = -(-3/2*((65/9)^(1/2)-1/3)) // : 1

w^2 = 3/2*((65/9)^(1/2)-1/3)

w^2 = 3/2*((65/9)^(1/2)-1/3) // ^ 1/2

abs(w) = (3/2)^(1/2)*((65/9)^(1/2)-1/3)^(1/2)

w = (3/2)^(1/2)*((65/9)^(1/2)-1/3)^(1/2) or w = -((3/2)^(1/2)*((65/9)^(1/2)-1/3)^(1/2))

w in { (3/2)^(1/2)*((65/9)^(1/2)-1/3)^(1/2), -((3/2)^(1/2)*((65/9)^(1/2)-1/3)^(1/2)) }

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