What is the sum of two consecutive even numbers if the difference of their squares is 84?

Problem restatementLet the even integers be x and x + 2. Given (x + 2)² − x² = 84, find x + (x + 2).

Concept/ApproachUse the identity (a + b)(a − b) = a² − b², or expand directly.

Step-by-step calculation (x + 2)² − x² = 4x + 4 = 84 4(x + 1) = 84 → x + 1 = 21 → x = 20 Sum = x + (x + 2) = 20 + 22 = 42

Verification/AlternativeSquares: 22² − 20² = 484 − 400 = 84, consistent.

Final Answer42