Question

If α, β are roots of x^2-2x-1=0 then α^3+β^3 is

Answer 1

Answer:

Step-by-step explanation:

let A^3 = t

=> A = t^(1/3)

putting this value of root in x^2 -2x -1 =0

=> t^(2/3) - 2t^(1/3) = 1

cubing on both sides,

=> t^2 - 8t - 6t=1 (by cubing identity)

=>t^2 - 14t -1 = 0

so t= <14 + sqroot(196+4)>/2 or <14 -sqroot(196=+4)>/2

roots are 7 + 5root2 and 7-5root2

so equation with such roots is

x2 - 14x - 1 = 0

and from here A^3 + B^3 = 14 sum of roots and your answer