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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
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The correct answer is:
less than 1
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.
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.
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