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Let a and b and 2x2 - 8x + 7 = x^2 - 4x + 13. be the roots of the quadratic. Compute a^3*b + a*b^3

 Apr 5, 2024
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 \(Compute\ a^3b + ab^3\)

 

\(2x^2 - 8x + 7 = x^2 - 4x + 13\\ x^2-4x-6=0\\ x=2\pm\sqrt{4+6}\\ x\in \{2-\sqrt{10}\ ,\ 2+\sqrt{10}\}=\{a,b\}\)

 

\(a^3b + ab^3\\ =(2-\sqrt{10})^3(2+\sqrt{10})+(2-\sqrt{10})(2+\sqrt{10})^3\\ \color{blue}=-168\)

 

laugh 

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 Apr 5, 2024

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