<p>No idea how to do it. The answer is 2.5</p>
<p>To simplify things, create new variables for x+y and x-y. We’ll use a and b.</p>
<p>a^2 - b^2 > 25 (look more familiar now?)</p>
<p>(a+b)(a-b) > 25</p>
<p>Now substitute the x’s and y’s back in:</p>
<p>(x+y+x-y)(x+y-x+y) > 25</p>
<p>(2x)(2y) > 25</p>
<p>4xy > 25</p>
<p>xy > 25/4</p>
<p>Since x<y, y will be least when it is equal to x, and when xy is as small as possible (i.e., when it’s 25). Thus, we can substitute y in for x and make the expression equal:</p>
<p>y^2 = 25/4</p>
<p>y = 5/2 = 2.5</p>
<p>^ Yeah I managed to get it down to 4xy => 25 but I didn’t quite reason out the last part. </p>
<p>Edit: Ahhh no wonder. I was thinking of scenarios in which x would be greater than y but I didn’t pay close enough attention to the inequality :(</p>
<p>4xy ≥ 25
Divide by 4 because you are solving for variable(s)
xy ≥ 6.25
Since y ≥ x, y can be any number that’s ≥ x. The answer is the SMALLEST y value possible. Which y value is smaller, the one bigger than x, or the one equal to x? The one equal to x. Since they are equal, you can change it to y^2 ≥ 6.25
The square root of 6.25 is 2.5</p>
<p>i see you have figured it out</p>