Question

Product of two consecutive integers is 29 more than their sum . Find the integers

Answer 1

Product of two consecutive integers is:

n(n+1)=n²+n

Sum of two consecutive integers is:

n+(n+1)=n+n+1=2n+1

What you have proclaimed:

n²+n=2n+1+29

n²+n=2n+30

n²+n-2n-30=0

n²-n-30=0

(n-6)(n+5)=0

Therefore n=6 or n=-5.

When n=6,

n+1=7

First answer: 6 and 7.

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When n=-5,

n+1=-4

Second answer: -4 and -5.