Question 11
If $a$ and $b$ are two different real numbers, solve the $$
\begin{aligned}
x+y & =1 \\
(a x+b y)^2 & \leq a^2 x+b^2 y
\end{aligned}
$$ system also solve the $$
\begin{aligned}
x+y & =1 \\
(a x+b y)^4 & \leq a^4 x+b^4 y
\end{aligned}
$$ system
\begin{aligned}
x+y & =1 \\
(a x+b y)^2 & \leq a^2 x+b^2 y
\end{aligned}
$$ system also solve the $$
\begin{aligned}
x+y & =1 \\
(a x+b y)^4 & \leq a^4 x+b^4 y
\end{aligned}
$$ system