If a,b,c are positive real numbers, then ab+c+bc+a+ca+b is
<32
≥32
>52
None of these
Explanation for correct option.
Given, a,b,c are positive real numbers
Now,
Arithmetic Mean of the term ≥inverse of the Arithmetic Mean of the it's inverse
Therefore,
a+b+cb+c+a+b+cc+a+a+b+ca+b3≥{b+ca+b+c+c+aa+b+c+a+ba+b+c3}-1a+b+cb+c+a+b+cc+a+a+b+ca+b3≥(23)-1a+b+cb+c+a+b+cc+a+a+b+ca+b3≥32a+b+cb+c+a+b+cc+a+a+b+ca+b≥92ab+c+bc+a+ca+b+3≥92ab+c+bc+a+ca+b≥92-3ab+c+bc+a+ca+b≥32
Hence, correct option is (B)