Question

The product of two consecutive integers is 98 more than the next integer. What is the largest of the three integers?

Answer 1

So the three integers are `10` , `11` , `12`

Explanation:

Let `3` consecutive integers be `(a-1),a and (a+1)`
Therefore
`a(a-1)=(a+1)+98`
or
`a^2-a=a+99`
or
`a^2-2a-99=0`
or
`a^2-11a+9a-99=0`
or
`a(a-11)+9(a-11)=0`
or
`(a-11)(a+9)=0`
or
`a-11=0`
or
`a=11`
`a+9=0`
or
`a=-9`
We will take only positive value So `a=11`
So the three integers are `10` , `11` , `12`