+0

# The value of the expression (2^(1004)+5^(1005))^2-(2^(1004)-5^(1005))^2 is $k\cdot10^{1004}$ for some positive integer $k$. What is $k$?

0
171
2
+211

The value of the expression (2^(1004)+5^(1005))^2-(2^(1004)-5^(1005))^2 is $k\cdot10^{1004}$ for some positive integer $k$. What is $k$?

Aug 16, 2020

#1
0

k = 16.

Aug 16, 2020
#2
+1

The LHS reduces to 2 x 10^1005

2 x 10^1005  =k * 10^1004

k =[2 x10^1005] / [10^1004] =2 x 10

k =20

Aug 16, 2020