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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.

 Jul 26, 2022
 #1
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a^3 + b^3 = 56.

 Jul 26, 2022
 #2
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a^3 + b^3 = (a + b)((a + b)^2 - 3ab)


Use vieta's formulas!

 

x^2 - 2x + 6 = 0 

 

a + b = 2

ab = 6

 

Plugging this in gives us

 

(2)(4 - 18) =  -28.

 Jul 26, 2022

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