<p>If 0<x<y (both="" should="" be="" "or="" equal="" to="" ")="" and="" (x+y)^2="" -="" (x-y)^2="">25 (Once again greater than or equal to) what is the least possible value of y?</x<y></p>
<p>Thanks</p>
<p>wow i was wondering about the same question!! this is from one of the sat practice tests right??</p>
<p>(X+Y)^2 = X^2 + 2XY + Y^2
(X-Y)^2 = X^2 - 2XY + Y^2</p>
<p>(X+Y)^2 - (X-Y)^2 = (X^2 + 2XY + Y^2) **-<a href=“X%5E2%20%5Bb%5D-%202XY%5B/b%5D%20+%20Y%5E2”>/b</a> = 4XY (squared terms cancel out)</p>
<p>4XY ≥ 25
Obviously since you want to minimize the value of y, you want 4XY to be as small as possible. The smallest it can be is 25.</p>
<p>4XY = 25
XY = 6.25</p>
<p>since 0≤x≤y, to minimize y, you want it to be as small as possible. The smallest it can be is x. So, x = y</p>
<p>XY = 6.25
XY = X^2 = Y^2 = 6.25
X = sqrt(6.25) = 2.5
Y = sqrt(6.25) = 2.5 <-ANSWER</p>
<p>I know this question may be a bit confusing. Just remember to use REASONING. There’s no magical formula or process that you have to memorize in order to answer this question. It requires logic and thinking.</p>
<p>thank you!!!</p>
<p>Thanks so much. I got it all the way down to xy=6.25 but then couldnt figure out what to do. thanks agian</p>
<p>that was a real good explanation crazybandit.</p>
<p>Linger the smallest value of y is when x=y so you can say its x(x) or y(y). That = x^2 or y^2 and then you solve.</p>