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If A and B are the roots of x^2 - 4x + 1 = 0, then find A^3 + B^3.

 Jun 21, 2020
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This is simple. x^2-4x+1 is not factorable so we plug it into the quadratic equation.

 

x=b±b24ac2ax=4±(4)24(1)(1)2(1)x=4±122x=4±232x=2±3

 

Cube the two roots.

 

(2+3)3+(23)3=52

 Jun 21, 2020

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