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What is the Sum of Two Consecutive Even Numbers, the Difference of Whose Squares is 84?

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Explanation

  • What is the sum of two consecutive even numbers.
  • The difference of whose squares is 84.

Let suppose the numbers are y and y + 2.

The difference of squares of y and y + 2 is 84

(y + 2)2 – y2 = 84 ________ (i)

By simplifying equation (i), we can easily figure out the value of both even numbers (20 and 22) and their sum (42).

To Find

Sum = ?

Solution

Let suppose

Numbers are y and y + 2.

According to the given conditions

(y + 2)2 – y2 = 84

(y2 + 4 + 4y) – y2 = 84

y2 + 4 + 4y – y2 = 84

4 + 4y = 84

4y = 84 – 4

4y = 80

y = 80/4

y = 20

Second Even Number = 20 + 2 = 22

Sum = 20 + 22 = 42

Sum = 42 answer

Conclusion

The sum of two consecutive even numbers, the difference of whose squares is 84 will be 42.

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