x^(4/3)-7x^(2/3)-10=0

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Solution for x^(4/3)-7x^(2/3)-10=0 equation: 


x in (-oo:+oo)

x^(4/3)-(7*x^(2/3))-10 = 0

x^(4/3)-7*x^(2/3)-10 = 0

t_1 = x^(2/3)

1*t_1^2-7*t_1^1-10 = 0

t_1^2-7*t_1-10 = 0

DELTA = (-7)^2-(-10*1*4)

DELTA = 89

DELTA > 0

t_1 = (89^(1/2)+7)/(1*2) or t_1 = (7-89^(1/2))/(1*2)

t_1 = (89^(1/2)+7)/2 or t_1 = (7-89^(1/2))/2

t_1 = (7-89^(1/2))/2

x^(2/3)-((7-89^(1/2))/2) = 0

1*x^(2/3) = (7-89^(1/2))/2 // : 1

x^(2/3) = (7-89^(1/2))/2

( (7-89^(1/2))/2 < 0 i 2/3 in (0:1) ) => x należy do O

t_1 = (89^(1/2)+7)/2

x^(2/3)-((89^(1/2)+7)/2) = 0

1*x^(2/3) = (89^(1/2)+7)/2 // : 1

x^(2/3) = (89^(1/2)+7)/2

x^(2/3) = (89^(1/2)+7)/2 // ^ 3

x^2 = ((89^(1/2)+7)^3)/8 // ^ 1/2

abs(x) = ((89^(1/2)+7)^(3/2))/(2*2^(1/2))

x = ((89^(1/2)+7)^(3/2))/(2*2^(1/2)) or x = -(((89^(1/2)+7)^(3/2))/(2*2^(1/2)))

x in { ((89^(1/2)+7)^(3/2))/(2*2^(1/2)), -(((89^(1/2)+7)^(3/2))/(2*2^(1/2))) }

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