Question

Formula of 1/alpha³+1/beta³ =​

Answer 1

Answer:

We know that α+β=−ba and αβ=ca.

The sum of the new roots is α+1β+β+1α=−ba+α+βαβ=−ba+−baca=−ba−bc=−bc+abac

The product of the new roots is (α+1β)(β+1α)=αβ+2+1αβ=2+ca+ac=2ac+a2+c2ac=(a+c)2ac .

The new equation is x2+bc+abacx+(a+c)2ac=0⇒acx2+b(a+c)x+(a+c)2=0