2/a+2/b+2/c
= 1/9 *(2/a+2/b+2/c)*(a+b+c)
=1/9*(6+ 2b/a +2c/a + 2a/b +2c/b +2a/c+2b/c)
=1/9*[6+(2b/a+2a/b )+(2c/a+2a/c)+(2c/a+2b/c)]
≥1/9* [6+2√(2b/a*2a/b)+2√(2c/a*2a/c)+2√(2c/a*2b/c)]
=1/9*(6+4+4+4)=2
2/a+2/b+2/c
= 1/9 *(2/a+2/b+2/c)*(a+b+c)
=1/9*(6+ 2b/a +2c/a + 2a/b +2c/b +2a/c+2b/c)
=1/9*[6+(2b/a+2a/b )+(2c/a+2a/c)+(2c/a+2b/c)]
≥1/9* [6+2√(2b/a*2a/b)+2√(2c/a*2a/c)+2√(2c/a*2b/c)]
=1/9*(6+4+4+4)=2