If y is any real number, then y² is always nonnegative (i.e. not negative).
Examples:
- y = -10 leads to y² = (-10)² = 100
- y = 0 leads to y² = (0)² = 0
- y = 7 leads to y² = (7)² = 49
There's no way to have y² be a negative value.
So everything relies on the 3p
If p > 0, then 3p > 0 after multiplying both sides by 3.
Therefore, p being positive means 3p is also positive.
Adding a positive number onto y² is some other positive number (either that value itself or larger).
Overall, y²+3p > 0 if p > 0