Question

If the reciprocal of the product of the two consecutive integers is 1/30 how do you find the two integers?

Answer 1

Then the product must be the reciprocal of `1//30` and that is `30` (reciprocal goes both ways).

Explanation:

The reciprocal of the reciprocal is the original number.

So we need `n*(n+1)=30`
You can try factoring `30` in different ways, but it will be clear that only `5and6` satisfy the condition of being consecutive.

Answer 2

`5,6 or -6,-5`

Explanation:

*Integers:* The numbers which are not fractional(like `26/9`) are called integers.

Let A, B be two consecutive numbers.

suppose A=n say.

Then B must be "n+1" as it is next number to A.

Product of two consecutive numbers=AB.

The reciprocal of the product of the two consecutive integers=`1/(AB)`

But, the reciprocal of the product of the two consecutive integers is 1/30.

From equality rule,
Ultimately,

`1/(AB)=1/30`

Just substitute assumed A,B values.

`1/(n(n+1))=1/30`

`=>1/(n^2+n)=1/30`

`=>n^2+n-30=0`

`=>n^2+6n-5n-30=0`

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

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

`=>n=5 | n=-6`

If `n=5`;

`A=5,`

`B=6`

If `n=-6:`

`A=-6`

`B=-5`