Simplifying, the equation you have is \(x^2 - 23x - 16 = 0\).
From Vieta's formulas, we have \(\begin{cases} a + b = 23\\ ab = -16 \end{cases}\).
Now, note that \(a^4 + b^4 = (a^2 + b^2)^2 - 2a^2 b^2 = ((a+b)^2 -2ab)^2 - 2(ab)^2\).
Can you continue from here?
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