<p>Please help me this Math question from 2007-2008 Practice Test.I know the answer but I would like to know how to do it .</p>
<p>If 0 ≤ x ≤ y and x + y 2 − x − y 2 ≥ 25, what
is the least possible value of y ?</p>
<p>May not be the best explanation since most of this required thinking (for me at least) rather than a specific equation.</p>
<p>Since you know x and y can be equal and you are looking the the lower value of y, it would make sense to keep x and y at the same value. If you think about it, having x and y at the same value would give you 0 for (x-y) part of the equation. Now just thinking of the square root of 25, which is 5 and split it in half to get the lowest possible number.</p>
<p>Horrible explanation, but its the best I can do for this problem.</p>
<p>If we simplify (x+y)^2 -(x-y)^2 then we are left with x^2+2xy+y^2-x^2+2xy-y^2 = 4xy.</p>
<p>So 4xy≥25 dividing by 4, xy≥6.25. To because we are given that 0 ≤ x ≤ y, the least possible value for y occurs when y=x. so y^2 ≤ 6.25 y = 2.5</p>
<p>Thank you !</p>