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1. What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?
Then,
(x + 2)2 - x2 = 84
⇔ 4x + 4 = 84
⇔ 4x = 80
⇔ x = 20
∴ Required sum
= x + (x + 2)
= 2x + 2
= 42
Solution:
Let the numbers be x and x + 2Then,
(x + 2)2 - x2 = 84
⇔ 4x + 4 = 84
⇔ 4x = 80
⇔ x = 20
∴ Required sum
= x + (x + 2)
= 2x + 2
= 42