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# Daily Question Contest 1

+5
802
9

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

Nov 11, 2015

#7
+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  !!!!   Nov 11, 2015

#1
+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...)

Nov 11, 2015
#4
+10

Simplifying the ratio: Nov 11, 2015
#5
+10

Let $$a = 20152016,$$ and we have

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

Nov 11, 2015
#6
0

Much the simplest Guest- well spotted!

Nov 11, 2015
#7
+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  !!!!   CPhill Nov 11, 2015
#9
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."

Nov 12, 2015