If =∣∣abcabcabcb2cc2aa2bc2bca2b2a∣∣=0,(a,b,c∈R) and are all different and nonzero), then prove that a+b+c=0.

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If ={|{array}{ccc} {a}{b}{c}&{b}^{{2}}{c}&{c}^{{2}}{b}{a}{b}{c

Question

If $= ∣ ∣ a b c a b c a b c b^{2} c c^{2} a a^{2} b c^{2} b c a^{2} b^{2} a ∣ ∣ = 0, (a, b, c \in R)$ and are all different and nonzero), then prove that $a + b + c = 0 .$

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Elijah Discussed

= ∣ ∣ a b c a b c a b c b^{2} c c^{2} a a^{2} b c^{2} b c a^{2} b^{2} a ∣ ∣ = 0, (a, b, c \in R)

and are all different and nonzero), then prove that

a + b + c = 0 .

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Question Text

= ∣ ∣ a b c a b c a b c b^{2} c c^{2} a a^{2} b c^{2} b c a^{2} b^{2} a ∣ ∣ = 0, (a, b, c \in R)

and are all different and nonzero), then prove that

a + b + c = 0 .