Final answer:
The inequality (y-1)(y+1) > y² is incorrect as shown by expanding the left side to y² - 1, which cannot be greater than y². The correct inequality is (y-1)(y+1) < y², which is true for any real number y.
Step-by-step explanation:
To prove the inequality (y-1)(y+1) > y², let's first expand the left side of the inequality:
- (y - 1)(y + 1) = y² + y - y - 1
- (y - 1)(y + 1) = y² - 1
Now we have y² - 1 > y². This inequality simplifies to -1 > 0, which is not true for any real value of y. Thus, it suggests that there might be an error or misunderstanding in the initial statement as it's given. Instead, if we consider (y-1)(y+1) = y² - 1, it is clear that for this expression to be greater than y², we must actually consider when y² - 1 < y².
This inequality is true since subtracting 1 from y² will always make it less than y² for any real value of y. Therefore, the correct statement is that (y-1)(y+1) < y² for all real numbers y.