If the expression can be resolved into two rational factors

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If the expression ax2+by2+cz2+2ayz+2bxz+2cxyax^2+by^2+cz^2+2ayz+2bxz+2cxy can be resolved into two rational factors, prove that a3+b3+c3=3abca^3+b^3+c^3=3abc.

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