If a+b+c=1 where a,b,c are non negative real number then find the maximum value of 10101(ab+bc+ca) - 12987abc

Question

Give positive numbers a, b and c are such that
ab + bc + ca + abc = 4,
What is the value of
1/a+2 + 1/b+2 + 1/c+2 = ?

Answer 1

the real numbers will have the values each = 1/3 for maximum value of the product ab+bc+ca
thus 10101(ab+bc+ca)-12987abc equals
10101/3-12987/27=3367-481=2886