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Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 6x + 1. Compute a^3 + b^3.

 Oct 15, 2022
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Compute a^3 + b^3.

 

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\(2x^2 - 8x + 7 = x^2 - 6x + 1\\ x^2-2x+6=0\\ x=1\pm \sqrt{1-6}\\ \color{blue}x\in \{1-i\sqrt{5},1+i\sqrt{5}\}\\ a=1-i\sqrt{5}\\ b=1+i\sqrt{5}\\a^3=-14+2\sqrt{5}i\\ b^3=-14-2\sqrt{5}i\\ \color{blue}a^3+b^3=-28\)

laugh  !

 Oct 15, 2022
edited by asinus  Oct 15, 2022

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