What is the sum of two consecutive even numbers, the difference of whose squares is 84?

One Answer on this Question

1. Let the numbers be x and x + 2.
   Then, (x + 2)2 – x2 = 84
   ⇒ 4x + 4 = 84
   ⇒ 4x = 80
   ⇒ x = 20.
   ∴ The required sum
   = x + (x + 2)
   = 2x + 2
   = 42

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