Question

Proving an inequality?

If a, b, and c are positive numbers and a+b+c=1, prove the inequality
`a*b+b*c+c*a ≥ 9*a*b*c`

Answer 1

The arithmetic mean is greater than the harmonic mean

Explanation:

`(a + b + c)/3 ge =3/(1/a+1/b+1/c)`
or
`ab + ac + bc ge 9abc`