can we find an exact solution? t^6 +4t^4 −12t^3 +24t^2 −24t+8=0


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Question Number 61140 by MJS last updated on 29/May/19

$can we find an exact solution ?$ $t^{6} + 4 t^{4} - 12 t^{3} + 24 t^{2} - 24 t + 8 = 0$
Commented by ajfour last updated on 04/Jun/19

$w h a t s t h e s o u r c e o f t h i s q u e s t i o n,$ $I s t h e r e a w a y t o s o l v e i t, a f t e r a l l$ $S i r ?$
	Answered by ajfour last updated on 30/May/19
	${t^2 (t^2 +2)^2 +20t^2 +8}^2 =144t^2 (t^2 +2)^2 let t^2 =s ⇒ {s(s+2)^2 +20s+8}^2 =144s(s+2)^2 ......$
	${t^{2} {(t^{2} + 2)}^{2} + 20 t^{2} + 8}^{2} = 144 t^{2} {(t^{2} + 2)}^{2}$ $l e t t^{2} = s$ $\Rightarrow {s {(s + 2)}^{2} + 20 s + 8}^{2} = 144 s {(s + 2)}^{2}$ $. . . . . .$
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