(adsbygoogle = window.adsbygoogle || []).push({}); Prove that if x and y are ....

1. The problem statement, all variables and given/known data

Prove that if x and y are distinct real numbers, then (x+1)^{2}=(y+1)^{2}if and only if x+y=-2. How does the conclusion change if we allow x=y?

2. Relevant equations

...

3. The attempt at a solution

Suppose x and y are real numbers. If x≠y then

x+2≠y+2

----> (x+2)/(y+2)≠1

----> (x+2)/(y+2)≠ x/y or y/x (since x/y=y/x=1)

----> (x+2)x=(y+2)y

or

(x+2)/x=(y+2)/y

----> (x+2)x=(y+2)y (since (x+2)/x=(y+2)/y ---> x=y)

----> x^{2}+2x=y^{2}+2y

---->x^{2}+2x+1=y^{2}+2y+1

---->(x+1)^{2}=(y+1)^{2}

----> x+1 = (y+1) or (-y-1)

----> x+1=-y-1 (since x+1=y+1 ---> x=y)

----> x+y=-2

?????

But I'm not sure if I've done everything it asked. I know for "P if and only Q," it needs to be proven that P--->Q and Q--->P, but it seems here that if P is (x+1)^{2}=(y+1)^{2}and Q is x+y=-2, I'm just kind of going in circles by proving the "if and only if" part. See what I'm saying?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove that if x and y are

**Physics Forums | Science Articles, Homework Help, Discussion**