0=x-7x^(1/7)

Solution for 0=x-7x^(1/7) equation:

x in (-oo:+oo)

0 = x-(7*x^(1/7)) // - x-(7*x^(1/7))

7*x^(1/7)-x+0 = 0

7*x^(1/7)-x = 0

t_1 = x^(1/7)

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

7*t_1-t_1^7 = 0

t_1*(7-t_1^6) = 0

-1*t_1^6 = -7 // : -1

t_1^6 = 7

t_1^6 = 7 // ^ 1/6

abs(t_1) = 7^(1/6)

t_1 = 7^(1/6) or t_1 = -7^(1/6)

t_1 = 0

t_1 = 0

t_1 = 7^(1/6)

x^(1/7)-7^(1/6) = 0

1*x^(1/7) = 7^(1/6) // : 1

x^(1/7) = 7^(1/6)

x^(1/7) = 7^(1/6) // ^ 7

x = 7^(7/6)

t_1 = -7^(1/6)

x^(1/7)+7^(1/6) = 0

1*x^(1/7) = -7^(1/6) // : 1

x^(1/7) = -7^(1/6)

( -7^(1/6) < 0 i 1/7 in (0:1) ) => x należy do O

t_1 = 0

x^(1/7)+0 = 0

x^(1/7) = 0

1*x^(1/7) = 0 // : 1

x^(1/7) = 0

x = 0

x in { 7^(7/6), 0 }