Vieta's is fun, so I'll post another problem!

Algebra Level 5

\[x^3-7x^2+5x+2=0\]

Given that \(a\), \(b\) and \(c\) are the roots of the above equation, find the value of \( \displaystyle \sum_{\text{cyc}} \dfrac{a^4}{bc+1}\).


Too hard? Here are some slightly easier problems.

Too easy? Try this then.

Give this problem a solution which is more elegant, faster or simpler than mine!
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