will be cqual, if either $$ b=0 $$, or $$ a^{3}+b^{2}+c^{3}-3 a b c-0 $$. If $$ a, b, c $$ arc rational and $$ a+b+c=0 $$, show that the roots of $$ (b+c-a) x^{2}+(c+a-b) x+ $$ $$ (a+b-c)=0 $$ are rational.

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Adkins Norton · Accepted Answer

The roots of the quadratic equation are rational because the discriminant is a perfect square of a rational number, and the roots can be expressed as rational expressions.

will be cqual, if either \( b=0 \), or \( a^{3}+b^{2}+c^{3}-3 a b c-0 \). If \( a, b, c \) arc rational and \( a+b+c=0 \), show that the roots of \( (b+c-a) x^{2}+(c+a-b) x+ \) \( (a+b-c)=0 \) are rational.

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will be cqual, if either \( b=0 \), or \( a^{3}+b^{2}+c^{3}-3 a b c-0 \). If \( a, b, c \) arc rational and \( a+b+c=0 \), show that the roots of \( (b+c-a) x^{2}+(c+a-b) x+ \) \( (a+b-c)=0 \) are rational.

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