Question 131
It shows that $$
(a x+b y)^{2} \leq a x^{2}+b y^{2}
$$ for any $x, y \in \mathbb{R}$ and any $a, b \in \mathbb{R}$ with $a+b=1,\ a, b \geq 0$. In what cases does equality occur?
(a x+b y)^{2} \leq a x^{2}+b y^{2}
$$ for any $x, y \in \mathbb{R}$ and any $a, b \in \mathbb{R}$ with $a+b=1,\ a, b \geq 0$. In what cases does equality occur?