1.

If alfa and beta are the roots of x^2-px+q =0 then alfa cube + beta cube is​

Answer»

ANSWER:

(p)(p^2-q)

Step-by-step explanation:

Alpha and beta are roots of x^2-px+q

Alpha*Beta= c/a = q/1

Alpha+Beta= -b/a = p/1

On SQUARING both sides we get,

(Alpha+Beta)^2 = p^2

Alpha^2+Beta^+2*Alpha*Beta = p^2

Alpha^2+Beta^2+ 2*q= p^2( Alpha*Beta=q)

Alpha^2+Beta^2 = p^2-2q

Alpha^3 + Beta^3 = (Alpha+Beta)(alpha^2-alpha*beta+beta^2)

                             =(p)(p^2-2q-q)

                             = (p)(p^2-q)

                           

So alpha^3+beta^3 = (p)(p^2-q)

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