<p>I have no idea how to start this. Help anyone? </p>
<p>If 0 <= x <= y and (x + )^2 - (x + y)^2 >= 25, what is the least possible value of y? </p>
<p>I know this formatting makes it sort of hard to read. But, thanks to anyone in advance who responds!</p>
<p>(x+y)^2-(x-y)^2 ≥ 25
difference of 2 squares:
((x+y)+(x-y))<em>((x+y)-(x-y)) ≥ 25
(2x)</em>(2y) ≥ 25
4xy ≥ 25
y ≥ x ≥ 0</p>
<p>if x is a big number, then y is also a big number because it is greater than or equal to it. So for y to be a small number, x also has to be a small number. For y to be the smallest possible number, it has to be equal to x. So you set x and y equal and solve for y</p>
<p>4y^2 ≥ 25
2y ≥ 5
y ≥ 2.5
y=2.5</p>
<p>You can also set x=y immediately, and change the inequality to an equation:</p>
<p>(2y)^2=25
4y^2=25
2y=5
y=5/2=2.5</p>