Question

x^2-4x+p=0
if 1/aplha cube +1/beta cube =64
find p
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Answer 1

Answer:

Step-by-step explanation:

Taking alpha as m and beta as n

m+n=4

mn=p

((1/m)+(1/n))^3=(1/m)^3+(1/n)^3+(3((1/m)+(1/n))/mn)

(m+n)^3/m^3n^3-3(m+n)/m^2n^2=(1/m)^3+(1/n)^3

64/p^3-12/p^2=64

16p^3+3p=16

p(16p^2+3)=16

p=16 or     16p^2+3=16

                 p^2=13/16

                 p=root(13)/4