Let a, b, c 0 and Delta = lef | vedclass

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Question

$c_{1} ightarrow c_{1}-c_{2}$

$\Delta=\left|\begin{array}{lll}{a} & {b} & {c} \ {b} & {c} & {a} \ {c} & {a} & {b}\end{a

Vedclass · Accepted Answer

$\Delta = 0 \Rightarrow\   a + b + c = 0$

Vedclass · Answer

$c_{1} ightarrow c_{1}-c_{2}$

$\Delta=\left|\begin{array}{lll}{a} & {b} & {c} \ {b} & {c} & {a} \ {c} & {a} & {b}\end{array}ight|=-\left[a^{3}+b^{3}+c^{3}-3 a b cight]$

Or $\Delta=-\frac{1}{2}(a+b+c)\left[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}ight]$

So $\Delta<0$

Also $\Delta=0 \Rightarrow \mathrm{a}=\mathrm{b}=\mathrm{c}(	herefore \mathrm{a}+\mathrm{b}+\mathrm{c}>0)$

Since $a+b+c 
eq 0$

Let $a, b, c > 0$ and $\Delta = \left| \begin{gathered}
a + b\,\,b\,\,c \hfill \\
b\, + \,c\,\,c\,\,\,a \hfill \\
c + a\,\,a\,\,b \hfill \\
\end{gathered} \right| ,$ then which of the following is not correct?

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