2*(y)^(1/2)+2=5*(y)^(1/4)

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Solution for 2*(y)^(1/2)+2=5*(y)^(1/4) equation: 


D( y )

y < 0

y < 0

y in <0:+oo)

2*y^(1/2)+2 = 5*y^(1/4) // - 5*y^(1/4)

2*y^(1/2)-(5*y^(1/4))+2 = 0

2*y^(1/2)-5*y^(1/4)+2 = 0

t_1 = y^(1/4)

2*t_1^2-5*t_1^1+2 = 0

2*t_1^2-5*t_1+2 = 0

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

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+5)/(2*2) or t_1 = (5-9^(1/2))/(2*2)

t_1 = 2 or t_1 = 1/2

t_1 = 1/2

y^(1/4)-1/2 = 0

1*y^(1/4) = 1/2 // : 1

y^(1/4) = 1/2

y^(1/4) = 1/2 // ^ 4

y = 1/16

t_1 = 2

y^(1/4)-2 = 0

1*y^(1/4) = 2 // : 1

y^(1/4) = 2

y^(1/4) = 2 // ^ 4

y = 16

y in { 1/16, 16 }

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