If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c ...

If `=|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R)` and are all different and nonzero), then prove that `a+b+c=0.`

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