A Hole In The Middle

Geometry Level 1

$\Large \underbrace{2^2 +2^2 + 2^2 + \cdots +2^2}_{12 \text{ times}} = \, ?$

8^2-2^2

8^2-4^2

8^2-6^2

6^2-4^2

2 solutions

Willydoo Willydoo
Mar 25, 2016

$12\times2^2=(16-4)\times(2^2) =(16\times2^2)-(4\times2^2) =(4^2\times2^2)-(2^2\times2^2) =8^2-4^2$

Mehul Arora
Mar 20, 2016

$= 12 \times 2^2 = 48 = (n+m)(n-m)$ [According to question]

$(n,m) = (13,11) , \color{#D61F06}{(8,4)} , (7,1) (\text {Unordered})$