Let `a, b, c` be real numbers such that `a + 2b + c = 4.` Find `max(ab + bc + ca).`

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 and c real numbers such that a^(2) + b^(2) + c^(2) = 1, then ab + bc + ca lies in the interval :

Let a,b and c be real numbers such that a7b+8c and 8a+4bc=7, then find a^(2)-b^(2)+c^(2)

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 and c are distinct positive real numbers and a^2 + b^2 + c^2 = 1, then ab + bc + ca is

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) =' pi'

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) =pi