Math ?

Test Preparation SAT Preparation
1

<p>If (x+y)(x^2-y^2)=0, which of the following must be true?
A. x=y
B. x=-y
C. x^2=y^2
D. x^2=-y^2
E. x^3=y^3</p>

<p>Answer is c.
Couldn't it be B as well..</p>

<p>Also would it help if I had graphed this problem?
Thanks a lot! =D</p>

2

<p>If the answer were B:
(x-x)(x^2-(-x)^2)=(0)(0-(-x)^2)
(-x)^2 is going to be a positive, and 0-(positive) is not 0.</p>

<p>edit:
I substituted y for -x, which is the same as substituting x for -y.</p>

3

<p>So why couldn’t we just set both things in parentheses equal to zero? I thought there was a rule that said we could…</p>

4

<p>oh wait,
my previous post is fail.
Disregard it, I’m sleepy and I have a crick in my neck.</p>

<p>Well…
I don’t know how to answer it now, lol.</p>

5

<p>Ahhh help please! D=</p>

6

<p>I seriously have no idea. I’m positive B works. Can someone correct me?</p>

7

<p>B COULD be the case. And A COULD be the case. But neither one MUST be the case. The one that MUST be the case would be choice C, which is true whether x=y or x=-y…</p>

<p>Also, I am sure this problem has been discussed at length on CC before…search for it…</p>

8

<p>Umm, do you have and advice on what the search terms should be? I searched (x+y)(x^2-y^2)=0 and I didn’t get any hits so I don’t really know what else to try. Maybe silverturtle or crazybandit or some other SAT master can save the day?</p>

9

<p>Bump bump bump</p>

10

<p>

Pckeller’s explanation (above) is correct. What do you still not get? I will try to elaborate. . . .</p>

<p>(x+y)(x^2-y^2)=0 (Factor the second term.)
(x+y)(x+y)(x-y)=0 (Set each of the 3 terms equal to 0 and solve for x.)</p>

<p>Based on the three factors above, x could either be positive y OR negative y. We can’t make a definitive statement as to what x must be (since there are two distinct options). If x = y, the statement “(x+y)(x+y)(x-y)=0” is true. If x = -y, that statement is also true. So we can’t say either of them MUST be true, because it can be either one.</p>

<p>So if we square the equation of each of the possibilities, here’s what happens:
x = y becomes x^2 = y^2
x = -y becomes x^2 = y^2</p>

<p>Therefore, we can make a definitive statement that x^2 = y^2. If x = y, then that statement is true. If x = -y, then that statement is true. Therefore, the statement x^2=y^2 MUST be true, since it encompasses all possibilities. x = -y only encompasses one possibility.</p>

11

<p>Thank you o Tree of Knowledge.</p>