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Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 5x + 3. Compute a^3*b + a*b^3.

 Jul 28, 2022
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First, simplify the equation to \(x^2 - 3x + 4 = 0\)

 

Note that \(a^3b + b^3 a = ab(a^2 + b^2) = ab((a+b)^2 - 2ab)\)

 

By Vieta's, \(a + b = {b \over a} = -{ -3 \over 1} = 3\) and \(ab = {c \over a} = 4\)

 

Can you take it from here?

 Jul 28, 2022

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