If t^3+1/t^3=8,then what is the value of t

Question

Original question is t+1/t=8, then find t^3 +1 /t^3? I have found the solution but I want to know how to find the value of question I asked. 

Answer 1

If t+1/t=8, then

t³+3t+3/t+1/t³=8³

t³+1/t³=8³-3(t+1/t)=8³-3*8=8(8²-3)=8*61=488.

t³+1/t³=488

 

Now denote u=t³. Then

u+1/u=488

u²-488u+1=0

You can solve for u and then find t but it gets a little complicated.

But if you want to find t from

t+1/t=8, then you multiply by t and get

t2-8t+1=0.

The answer is

t₁=4-√15, t₂=4+√15.