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Found problems: 2

2021 Science ON grade VII, 3
Tags: inequality , newton sums , symmetric sums , algebra
Are there any real numbers $a,b,c$ such that $a+b+c=6$, $ab+bc+ca=9$ and $a^4+b^4+c^4=260$? What about if we let $a^4+b^4+c^4=210$? [i] (Andrei Bâra)[/i]

2021 Science ON all problems, 3
Tags: algebra , inequality , symmetric sums , newton sums
Are there any real numbers $a,b,c$ such that $a+b+c=6$, $ab+bc+ca=9$ and $a^4+b^4+c^4=260$? What about if we let $a^4+b^4+c^4=210$? [i] (Andrei Bâra)[/i]