Answer
. Use a proof by contradiction to show that there is no rational number r for which r^3 + r + 1 = 0. [Hint: Assume
that r = a/b is a root, where a and b are integers and a/b
is in lowest terms. Obtain an equation involving integers
by multiplying by b^3. Then look at whether a and b are
each odd or even.]
Work Step by Step
So from figure 1 and 2 we see that the actual statement is true.
Hence it is proved that there is no rational number r for which r^3+r+1 = 0
