Question

Prove that alphav=3 alpha l

Answer 1

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Note that αα and ββ are roots of the quadratic equation: z2−( Sum of Roots )+ Product of Roots =0⟹z2−4z+6=0z2−( Sum of Roots )+ Product of Roots =0⟹z2−4z+6=0.

Note as, α2−4α+6=0α2−4α+6=0 (because αα satisfies the quadratic), we can easily see that :

α3=4α2−6α=4(4α−6)−6α=10α−24