Answer:
2
Explanation:
t + 1/t = 2
OK just looking at the equation, if you don't have to show work, if you guess and try t=1 you'll see 1 + 1/1 = 2 works, so t must be 1, and 1^2+1/(1^2) = 2. So the final answer is 2.
If you have to show work, t+1/t=2 is t^2+1=2t, t^2-2t+1=0, solving for t using the quadratic formula, you will get t = 1.
Then you can plug it into t^2 + 1/(t^2) to get 1^2+1/(1^2) = 1+1 = 2.