<p>If 0 <= (less than or equal to) x <= (less than or equal to) y and (x+y)^2 - (x-y)^2 >= 25, what is the least possible value of y?</p>
<p>You see the difference of two squares, so try factoring</p>
<p>(x+y)^2 - (x-y)^2 >= 25
[(x+y) + (x-y)][(x+y) - (x-y)] >= 25
[2x][2y] >=25
4xy >= 25</p>
<p>It asks what is the least possible value of y. To minimize y, we need to maximize x. x is largest when it’s equal to y (since 0 <= x <= y), so let x = y.</p>
<p>4y^2 >= 25
y^2 >= 25/4
y >= 5/2</p>
<p>(x+y)^2 = x^2 + 2xy + y^2</p>
<p>(x-y)^2 = x^2 - 2xy + y^2</p>
<p>subtract from each other</p>
<p>u get</p>
<p>4xy >= 25</p>
<p>which is basically</p>
<p>4xy = 25</p>
<p>xy = 6.25</p>
<p>y has to be at least 2.5</p>