The roots of the equation $x^2-4x+2=0$ are $\alpha$ and $\beta$. Without solving the equation,

Question

The roots of the equation $x^2-4x+2=0$ are $\alpha$ and $\beta$. Without solving the equation, find the value of each of the following. $\alpha^3+\beta^3$ $\dfrac{1}{\alpha-1}+\dfrac{1}{\beta-1}$

Accepted Answer

(a) $40$ (b) $-2$

Sum of cubes and shifted reciprocals

Sum of cubes and shifted reciprocals

Solution:

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