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If a b c are real and positive numbers such as 1/a+1+1/1+b+1/1+c=1. Proove that abc smaller than and equal 1/8

If a b c are real and positive numbers such as 1/a+1+1/1+b+1/1+c=1. Proove that abc smaller than and equal 1/8

Grade:10

1 Answers

Arun
25750 Points
6 years ago
a, b and c are positive real numbers, therefore each of the three fractions mentioned in the equation is less than 1. You have the following three inequalities. The maximum value of each a,b and c is attained (Separately) when the other two are zero.
 
a/a+1 
b/b+1 
c/c+1 
 
a/a+1 = 1/3
a = b= c = 1/2
So
a*b*c = 1/8

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