Uchy's Meap Volue rove numbers and (infs on ntuble pori ive murobers, then a M Sish da

Question

Question

Answer 1

Answer #1

Answer:

We will define M according to the following equation:

$aiyi aiXi where xi-$

Note then that since all the $y_i$ are positive,

$に!$

Then, we have to show that $min a, ^ M< max$ .

We see that:

$M=$

Since by definition of the maximum, $max a; > avi$ .

Similarly, we see that:

$lSiSn i= 1 i-1 i-1$

Since by definition of the minimum $min ai S aiV$

Hence, we get that $min a, ^ M< max$ , for M defined as in the start of the answer.

Answer 2

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