Problem solving skill

(1)You are given odd numbers 1,3,5,7 and 9. Can you get 2,4,6 and 8  with any three same or different numbers using addition and subtraction only.?

It is not possible. Sum of any three odd numbers will always be odd., can never be even.

(2)  x⁵ + x⁴ + x³ + x² + x + 1= 0. Find the value of x.

The given expression can be written as x (x⁴ + x³ + x² + x + 1) = -1.There are two possibilities.

x = 1 and (x⁴ + x³ + x² + x + 1) = -1

x = -1 and (x⁴ + x³ + x² + x + 1) = 1

The former solution is not valid as (x⁴ + x³ + x² + x + 1) ≠ -1 if x =1.x = -1, satisfy both the condition.