An Application of AM-GM Inequality

#mathonshorts #shorts

Find max value using AM-GM Inequality, which states that a+b ≥ 2 sqrt(ab)

[thinkinginmath]

For \( \sqrt{y} \):
Using AM-GM for \( y \) and \( \frac{1}{4} \):
\[ \frac{y + \frac{1}{4}}{2} \geq \sqrt{y \cdot \frac{1}{4}} \]
\[ y + \frac{1}{4} \geq \sqrt{y} \]

For \( \sqrt{z} \):
Similarly, using AM-GM for \( z \) and \( \frac{1}{4} \):
\[ z + \frac{1}{4} \geq \sqrt{z} \]
by choosing 1/4 as one of the numbers in our AM-GM application, we strategically obtain the desired square root terms on the right side of the inequality. The choice is not arbitrary but is made to fit the structure of the problem and align with our goal of maximizing the given expression.

[percussion]

Ok, you have zero comments and a few likes. Here's the problem, wth are you talking about? Max value that x +root y + root z equals? Why that? Where did 1/4 come from?
How does this relate to (a+b)/2 > root(ab)?
No context, nothing explained, if your trying to show cool math or educate this isn't it.