Since (21)^2=222+1=322, 6+42=2(3+22)=2(2+1)=2+2.Similarly, 6-42=2(2-1)=2-2.Therefore, 6+42+6-42=(2+2)+(2-2)=4.

jmc

algebra senior

Problem

Simplify

6 + 42 + 6 - 42 .

Solution

Since

(2 \pm 1)^{2} = 2 \pm 22 + 1 = 3 \pm 22

6 + 42 = 2 (3 + 22) = 2 (2 + 1) = 2 + 2 .

Similarly,

6 - 42 = 2 (2 - 1) = 2 - 2 .

Therefore,

6 + 42 + 6 - 42 = (2 + 2) + (2 - 2) = 4 .

Final answer