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Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 + 15x + 23. Compute a^4 + b^4.

 Apr 11, 2024
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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?

 Apr 11, 2024

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