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Katyanochek1 [597]
3 years ago
6

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

t.
Mathematics
1 answer:
Montano1993 [528]3 years ago
8 0
If a,b,c are the 3 positive integers
1/a +1/b +1/c > 6/abc
(bc+ac+ab)/abc >6/abc so
(bc+ac+ab)>6
The lowest positive integers that are different are 1,2,3 so the lowest value that (bc+ac+ab) could have is 1•2+2•3+1•3=2+6+3= 11 therefore
1/a +1/b +1/c > 6/abc is true
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