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

ab + bc + ca + abc = 4 is true only when a = b = c = 1
therefore
1/a+2 + 1/b+2 + 1/c+2 = 1/3 + 1/3 + 1/3 = 1.