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The numbers are 12 and 14.

Q: What are two consecutive positive even numbers the sum of whose squares is 340?

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12 and 13

The numbers are 8 and 9.

6,7,8 those numbers squared are 36,49,64 which add to 149

Consecutive numbers are whole numbers whose difference is 1.

Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.

Related questions

The numbers are 12 and 14.

8

The numbers are 13 and 14.

15 and 16

17 and 18

62 and 63

12 and 13

12 and 13 (and you may note that 12+13 = 25)

The numbers are 8 and 9.

6,7,8 those numbers squared are 36,49,64 which add to 149

The difference between the squares of two consecutive integers j and j+1 is |2j+1|. There are therefore two such pairs where this quantity is 17:-9 and -88 and 9

Consecutive numbers are whole numbers whose difference is 1.