If and are all different and if vmatrix a & a^2 & 1+a^3 b & b^2 & 1+b^3 c & c^2 &…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

If a,ba, b and cc are all different and if ∣aa21+a3bb21+b3cc21+c3∣=0, prove that abc=−1.\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0, \text{ prove that } abc = -1.

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