If $a, b, c$ are distinct positive real numbers and $a^2+b^2+c^2=1$, then the value of $a b+b c+c a$ is
If $a, b, c$ are distinct positive real numbers and $a^2+b^2+c^2=1$, then the value of $a b+b c+c a$ is
less than 1
greater than 1
equals to 1
any real number
Solution
Given, $a, b$ and $c$ are positive distinct real number.
Also, $a^2+b^2+c^2=1$
As square of a number is also positive, so
$\begin{aligned}
& 0 < a^2, b^2, c^2 < 1 \\
& \Rightarrow 0 < a, b, c, < 1
\end{aligned}$
$\therefore$ Values of $a b+b c+c a$ is less than one.