If (a^2 + b^2 + c^2 = 1 ) then the range of ab+bc+ca is | Mathematics | SolveeIt

If $a^2 + b^2 + c^2 = 1$ then the range of ab+bc+ca is

$[ 1 , \infty )$

$\left[ \frac{-1}{2} , \infty \right]$

$\left( - \frac{1}{2} ,1 \right)$

$\left[ \frac{-1}{2} , 1 \right]$

Answer

$\left[ \frac{-1}{2} , 1 \right]$

Explanation

If $a^2 + b^2 + c^2 = k$ then $ab+ bc+ ca \, \in \left[ - \frac{k}{2} , k \right]$

Mathematics Question on Relations and functions