Question

Algebra 2---Please help with this problem!!! Will give medals and hugs!

Show that the sum of the reciprocals of three different positive integers is greater than 6 times the reciprocal of their product.

Answer 1

You have
\[\frac{1}{a} + \frac{1}{b}+\frac{1}{c} > \frac{6}{abc}\]
Add the fractions on the left first

Answer 2

3/abc ?

Answer 3

How did you get 3 in the numerator? Get common denominators on each of the fractions then add them

Answer 4

How do you do that with letters?

Answer 5

They are variables for the three different positive integers. You don't evaluate them.

Answer 6

So you could just replace it with 1,2,3 ?

Answer 7

You want to prove it for any three numbers so you leave them as variables.

Answer 8

How do you do that?

Answer 9

\[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{ab+ac+bc}{abc}\]

Answer 10

do your real job is to show that \(ab +ac+bc>6\) which is easy enough since the smallest possible different positive integers are 1, 2, and 3

Answer 11

clear or no?

Answer 12

So what is the answer? I'm confused on how you get that.

Answer 13

first of all i added up the fractions

Answer 14

here lets do it this way
what are the three smallest possible positive integers?

Answer 15

1,2, and 3 right?

Answer 16

@satellite73