Timed Quant Practice #5 Medium

Can someone explain where I went wrong? I tried to simplify the problem by taking the root of both, which gave me x + 1/x = root7, so I said they were equal to each other. How would you look at this and know to manipulate QC, like Greg did?

how did you arrive at x + 1/x = √ 7

I took the root of the entire equation…I may have done it wrong. But I said root of x2 is x, root of 1/x2 is 1/x, and then 7 is just root7.

According to your logic,
9 + 16 = 25, that means 3 + 4 = 5

Here is a hint of why it does not work:

Let us assume (a + b) = c
Then
(a+b)^2 = c^2 => a^2 + b^2 + 2ab = c^2