Q) The sum of the squares of three consecutive even numbers is 596. Find the numbers.

ICSE Specimen Question Paper – 2026

Step 1: Let’s start by considering middle number as X
Hence, preceding even number will be (X – 2) and succeeding even number will be (X + 2).

Step 2: By the given condition, sum of the squares of these 3 numbers is 596
(X – 2)² + X² + (X + 2)² = 596
X² – 4 X + 4 + X² + 4 X + 4 = 596
3X² + 8 = 596
3 X² = 596 – 8 = 588
X² = 588/3 = 196 = 14²
X = 14
X – 2 = 14 – 2 = 12
X + 2 = 14 + 2 = 16
Therefore the three consecutive even numbers are 12, 14 and 16.

Check: 12² + 14² + 16² = 144 + 196 + 256 = 596
Since it satisfies the given condition, hence our answer is correct.

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