The product of two consecutive even integers is 10 less than 5 times their sum. find the two integers

Question

Carmelo Hayden

Mathematics

13 January, 18:43

The product of two consecutive even integers is 10 less than 5 times their sum. find the two integers

+1

Answers (2)

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Sheridan · Answer 1

Let a=2k and b = (2k+2) such that ab=5 (a+b) - 10

That is, 2k (2k+2) = (10k+10k+10) - 10.

Thus, 4k^2+4k=20k.

4k^2-16k=0

4k (k-4) = 0

k=0,4

That implies 4*6=5 (4+6) - 10 or

0*2=5 (0+2) - 10

I believe 0 and 2 are the only values which work.

Elliott Stafford · Answer 2

Elliott Stafford 13 January, 19:03

0

The integers are 3 and 5