In Example 8, the question was

(ZIML Varsity January 2019) Let $x$ be a real number, find the maximum value of

$$\sqrt{4x-3} + \sqrt{2-x},$$

rounded to the nearest tenth if necessary.

The solution given in the video was to decompose $\sqrt{4x-3}$ into 4 parts, but instead couldn't you have just factored out the 4 to get $2\sqrt{x-\frac{3}{4}}$ and done Cauchy with $a_1 = 2,a_2=1,b_1 = \sqrt{x-\frac{3}{4}},b_2 = \sqrt{2-x}$? I think this works but I want to confirm that it does. I got the same answer in the video doing this.