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Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = 0. Compute a^3 + b^3.

 Mar 1, 2023
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By the quadratic formula, the solutions are \(\dfrac{7 \pm i \sqrt{7}}{4}\)

 

Then \(a^3 + b^3 = \left( \dfrac{7 + i \sqrt{7}}{4} \right)^3 + \left( \dfrac{7 - i \sqrt{7}}{4} \right)^3 = \dfrac{49}{8}\)

 Mar 2, 2023

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