kaylahill14oyr4nf kaylahill14oyr4nf

01-11-2017
Mathematics

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

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ChaosAgent ChaosAgent

01-11-2017

The integers are 3 and 5

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MathisLif3 MathisLif3

01-11-2017

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.

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