Determine the three roots x_1,x_2,x_3 of x^3-6x-9=0. Use Lagrange’s procedure to find the sixth-degree equation satisfied by y, where x = y + 2/y. Determine all six solutions of this equation and express each explicitly as 1/3(x′ + ωx′′ + ω2x′′′), where (x′, x′′, x′′′) is a permutation of (x_1,x_2,x_3 ) and ω is a complex root of x^3-1=0. a) Substitute for x using x=y+2/y and multiply both sides of the equation by y^3 to create a 6th degree equation: b) Substitute r=y^3 and solve the resulting quadratic equation in r. c) Given the 2 solutions, r_1 and r_2, of the quadratic equation, the 6 solutions of the 6th degree equation are ∛(r_1 ),ω∛(r_1 ),ω^2 ∛(r_1 ),∛(r_2 ),ω∛(r_2 ),ω^2 ∛(r_2 ) where ω=(-1+√(-3))/2. Find the 3 solutions to the original equation (in terms of ω) using x_1=∛(r_1 )+∛(r_2 ),x_2=ω∛(r_1 )+ω^2 ∛(r_2 ) and x_3=ω^2 ∛(r_1 )+ω∛(r_2 )