Suppose a, b, and care positive numbers such that `a+b+ c= 1`. Then the maximum value of `ab + bc + ca` is

Let a,b and c be real numbers such that a+2b+c=4. Find the maximum value of (ab+bc+ca)

If a,b,c are distinct positive real numbers and a^(2)+b^(2) +c^(2)=1 then the value of ab+bc+ca is-

If a, b, c are positive number satisfying 4ab + 6bc + 8ca = 9, then find the greatest value of (abc).

If the product of three positive real numbers say a,b,c be 27, then the minimum value of ab+bc+ca is equal to

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

If a,b,c are unit vectors such that a+b+c=0 , then find the value of a.b+b.c+c.a .