111^2 + 131^2 = ?

Answer 1

Favourite answer

(121 - 10)^2 + (121 + 10)^2 =>

121^2 - 2 * 121 * 10 + 10^2 + 121^2 + 2 * 121 * 10 + 10^2 =>

2 * 121^2 + 2 * 10^2 =>

2 * (121^2 + 10^2) =>

2 * (14641 + 100) =>

2 * 14741 =>

29482

Hey Puzzling, before you TD others, you should probably check your numbers again.

Answer 2

111^2 + 131^2 = 29482

The structure of the problem suggests you may want to try some algebra on it. 

111 = 121 - 10

131 = 121 + 10

a = 121 = 11^2

b = 10

(a-b)^2 + (a+b)^2

= 2(a^2 + b^2)

a^2 = 11^4 = (10+1)^4

using the binomial theorem this is

1*10^4 + 4*10^3 

+ 6*10^2 + 4*10 + 1

= 14641

Or just use Pascal’s triangle. 

b^2 = 100

2(14641 + 100)

= 29282 + 200

= 29482

This allows you to do the problem using only mental math plus some algebra. 

Answer 3

111 squared plus 131 squared equals 29,482

Answer 4

29,482                

Answer 5

111² + 131²

= 12321 + 17611

= 29932