Question

The sum of the squares of three consecutive positive even numbers is 12296. Find the product of the three numbers divided by 8.

Answer 1

x² + (x + 2)² + (x + 4)² = 12,296

x² + x² + 4x + 4 + x² + 8x + 16 = 12,296

3x² + 12x + 20 = 12,296

3x² + 12x = 12,276

x² + 4x = 4,092

x² + 4x + 4 = 4,096

(x + 2)² = 4,096

x + 2 = 64

x = 62

The numbers are 62, 64, and 66.

(62 × 64 × 66) ÷ 8 = 32,736