Question

Plz help asap!!

Ally has 3 positive integers. She adds their reciprocals and gets a sum of 1. What is the product of her integers.

Thanks!!

Answer 1

the integers are x,y,z

their reciprocals are
`(1)/(x)`,
`(1)/(y)`, and
`(1)/(z)`

the sum is 1
hmm
remember, a/a=1 when a=a


`(1)/(x)+(1)/(y)+(1)/(z)=`

`(yz)/(xyz)+(xz)/(xyz)+(xy)/(xyz)=`

`(yz+xz+xy)/(xyz)=1`
therefor
yz+xz+xy=xyz
doesn't help much

different integers
ah, hum
the only way I can see is trial and error

find 1/x for x=2,3,4,5,6,7,8,9, etc and evaluate
1/2=0.5
1/3=0.3333
1/4=0.25
1/5=0.2
1/6=0.166666666
1/7=0.14285714285714285714285714285714
1/8=0.125
1/9=0.11111111111
1/10=0.1
1/11=0.090909090909090909
hum, experimentation tells us that it's probably not going to be 1/7
try adding the numbers and see which ones add to 1
hmm
ah ha

1/2+1/3+1/6=3/6+2/6+1/6=6/6=1


the integers are 2,3,6
their product is 2*3*6=36