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

2 Answers
Jul 5, 2015

Answer:

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.

Jul 7, 2015

Answer:

#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#