2x^2*y-y^6=(x)^1/3

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Solution for 2x^2*y-y^6=(x)^1/3 equation: 


x in (-oo:+oo)

2*x^2*y-y^6 = (x^1)/3 // - (x^1)/3

2*x^2*y-((x^1)/3)-y^6 = 0

2*x^2*y-(x/3)-y^6 = 0

2*x^2*y-1/3*x-y^6 = 0

DELTA = (-1/3)^2-(2*4*y*(-y^6))

DELTA = 1/9-8*y^7

1/9-8*y^7 = 0

-8*y^7 = -1/9 // : -8

y^7 = 1/72

y^7 = 1/72 // ^ 1/7

y = (1/72)^(1/7)

DELTA = 0  <=>  t_1 = (1/72)^(1/7)

x = 1/3/(2*2*y) i y = (1/72)^(1/7)

x = 1/12*y^-1 i y = (1/72)^(1/7)

( x = ((1/9-8*y^7)^(1/2)+1/3)/(2*2*y) or x = (1/3-(1/9-8*y^7)^(1/2))/(2*2*y) ) i y > (1/72)^(1/7)

( x = ((1/9-8*y^7)^(1/2)+1/3)/(4*y) or x = (1/3-(1/9-8*y^7)^(1/2))/(4*y) ) i y > (1/72)^(1/7)

y-(1/72)^(1/7) > 0

y-(1/72)^(1/7) > 0 // + (1/72)^(1/7)

y > (1/72)^(1/7)

x in { 1/12*y^-1, ((1/9-8*y^7)^(1/2)+1/3)/(4*y), (1/3-(1/9-8*y^7)^(1/2))/(4*y) }

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