Question

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

Answer 1

Then(x+2)2−x2=84Then(x+2)2−x2=84x2+4+4x−x2=84x2+4+4x−x2=844x+4=844x+4=844x=84−44x=84−44x=804x=80x=20x=20The required sum=x+(x+2)=2x+2=2×20+2=42

Answer 2

Let the numbers be x and x + 2.

(x + 2)^2 - x^2 = 84

 4x + 4 = 84

 4x = 80

x = 20.

 The required sum = x + (x + 2) = 2x + 2 = 42the sum of two consecutive even numbers, the difference of whose squares is 84 IS 42.