Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 + 15x + 23. Compute a^4 + b^4.
Simplifying, the equation you have is x2−23x−16=0.
From Vieta's formulas, we have {a+b=23ab=−16.
Now, note that a4+b4=(a2+b2)2−2a2b2=((a+b)2−2ab)2−2(ab)2.
Can you continue from here?
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