+0  
 
+5
572
9
avatar+349 

The question isss:

 

\(\frac{20152016^2}{20152015^2+20152017^2-2}=?\)

Details:

1. This contest will be done daily

2. The first 3 correct answers win

3. The 3 winners will be in the next question

Mathhemathh  Nov 11, 2015

Best Answer 

 #7
avatar+89876 
+10

[20152016^2]  / ( [ 20152015^2]   + [20152017^2]  - 2 ] )  =

 

[20152016^2] / ( [ 20152016 - 1]^2 + [ 20152016 + 1]^2 - 2 )  =

 

[20152016^2] /( 20152016^2 - 2(20152016) + 1 + 20152016^2 + 2(20152016) + 1  - 2 )   =

 

[20152016^2] / [ 2(20152016^2]  =

 

1/2

 

P.S.  - I did NOT "peek" at any other answer before I did mine.....scout's honor  !!!!

 

 

cool cool cool

CPhill  Nov 11, 2015
 #1
avatar+349 
+5

4. If the amount of people who solved it does not reach 3, the nearest answer will be picked

 

(sorry I forgot to add this rule...)

Mathhemathh  Nov 11, 2015
 #3
avatar
+5

0.5

Guest Nov 11, 2015
 #4
avatar+27042 
+10

Simplifying the ratio:

 

ratio

Alan  Nov 11, 2015
 #5
avatar
+10

Let \(a = 20152016, \) and we have

 

\(\displaystyle \frac{a^{2}}{(a-1)^{2}+(a+1)^{2}-2}=\frac{a^{2}}{(a^{2}-2a+1)+(a^{2}+2a+1)-2}=\frac{a^{2}}{2a^{2}}=\frac{1}{2}\).

Guest Nov 11, 2015
 #6
avatar+27042 
0

Much the simplest Guest- well spotted!

Alan  Nov 11, 2015
 #7
avatar+89876 
+10
Best Answer

[20152016^2]  / ( [ 20152015^2]   + [20152017^2]  - 2 ] )  =

 

[20152016^2] / ( [ 20152016 - 1]^2 + [ 20152016 + 1]^2 - 2 )  =

 

[20152016^2] /( 20152016^2 - 2(20152016) + 1 + 20152016^2 + 2(20152016) + 1  - 2 )   =

 

[20152016^2] / [ 2(20152016^2]  =

 

1/2

 

P.S.  - I did NOT "peek" at any other answer before I did mine.....scout's honor  !!!!

 

 

cool cool cool

CPhill  Nov 11, 2015
 #9
avatar+93654 
0

Hey guest, thanks for that.

 

Why don't you join up.  We would love that!

We would really like you to present a regular contest question but it would be even better still if it belonged to your username.

If you really do not want to do this for some reason then it would be good if you identified yourself in the first line or heading.

Like for instance.

"Bob's daily question contest."

Melody  Nov 12, 2015

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