Math Question (Level 5 Difficulty)

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1

<p>Please help me solve this question, any help appreciated. (I think there may be a way to solve it using derivatives as well)</p>

<p>if 0 ≤ x ≤ y and (x + y)² - (x - y)² ≥ 25, what is the least possible value of y?</p>

2

<p>=(x² + 2xy + y²) – (x² – 2xy + y²) ≥ 25
= x² + 2xy + y² - x² + 2xy - y² ≥ 25
= 4xy ≥ 25
= xy ≥ 6.25</p>

<p>I think least value of y=0 since you mentioned 0 ≤ x ≤ y.</p>

3

<p>Your approach is similair to the one I took, but the problem is look at the final statement:</p>

<p>xy ≥ 6.25
if y = 0 then xy = 0, and 0 is not greater than or equal to 6.25. Therfore 0 can’t be the answer. Neither x nor y can be equal to 0.</p>

4

<p>Just from plugging in integers through trial and error, I got 3 (with the statement being true assuming x=3 and y=3), but this is one of those questions where one should look at the answer choices as well as the question (unless it was in that fill-in-the-blank mini-section).</p>

<p>EDIT: A few minutes later - I realized that it’s 2.5. You want x as close to y as possible, but x+y must be more than or equal to 5.</p>

5

<p>This is a student-produced answer question so no answer choices, and your right the answer is 2.5. Is there a systematic approach to this question though?</p>

6

<p>btw
does the question mention whether x & y are integers or not?</p>

<p>because if they are not then y can be = 0.00000001, or something like that.</p>

7

<p>No it does not say anything about Integers, the question in the first post is the full question.</p>

8

<p>is this sum from Barrons?</p>

9

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/1004870-intesting-math-problem.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/1004870-intesting-math-problem.html&lt;/a&gt;&lt;/p&gt;

10

<p>(x+y+x-y)(x+y-x+y)>=25
2x(2y)>=25
4xy>=25
xy>=25/4</p>

<p>since y>=x u can take the sq root of 25/4
so least value of y is 5/2 = 2.5</p>

11

<p>Yeah qwerfsad is right. Remember this part: x ≤ y. The least possible value of y that follows that is x = y. xy ≥ 6.25 would then be y^2 ≥ 6.25. Then just take the square roots and you get 2.5.</p>

12

<p>oh ok, I get it, Thankyou for your assistance everyone.</p>