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D( t )
t^3-343 = 0
t^3-343 = 0
t^3-343 = 0
1*t^3 = 343 // : 1
t^3 = 343
t^3 = 343 // ^ 1/3
t = 7
t in (-oo:7) U (7:+oo)
(t^3-(7*t^2)-(7*t)+49)/(t^3-343) = 0
(t^3-7*t^2-7*t+49)/(t^3-343) = 0
t^3-7*t^2-7*t+49 = 0
t^3-7*t^2-7*t+49 = 0
{ 1, -1, 7, -7, 49, -49 }
1
t = 1
t^3-7*t^2-7*t+49 = 36
1
-1
t = -1
t^3-7*t^2-7*t+49 = 48
-1
7
t = 7
t^3-7*t^2-7*t+49 = 0
7
t-7
t^2-7
t^3-7*t^2-7*t+49
t-7
7*t^2-t^3
49-7*t
7*t-49
0
t^2-7 = 0
DELTA = 0^2-(-7*1*4)
DELTA = 28
DELTA > 0
t = (28^(1/2)+0)/(1*2) or t = (0-28^(1/2))/(1*2)
t = 7^(1/2) or t = -7^(1/2)
t in { -7^(1/2), 7^(1/2), 7}
(t+7^(1/2))*(t-7^(1/2))*(t-7) = 0
((t+7^(1/2))*(t-7^(1/2))*(t-7))/(t^3-343) = 0
( t+7^(1/2) )
t+7^(1/2) = 0 // - 7^(1/2)
t = -7^(1/2)
( t-7 )
t-7 = 0 // + 7
t = 7
( t-7^(1/2) )
t-7^(1/2) = 0 // + 7^(1/2)
t = 7^(1/2)
t in { 7}
t in { -7^(1/2), 7^(1/2) }
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