Question

x=2+2^1/3+2^2/3thanx^3-6x^2+6x than faind

Answer 1

x=2+2^2/3+2^1/3 ,

Let 2^1/3=p
x=2+p^2+p
x-2=p^2+p……………….(1)

cubing both sides

x^3–8–3.x.2.(x-2)=p^6+p^3+3.p^2.p.(p^2+p) , put (p^2+p)= (x-2)from eq.(1).
x^3–8–6x^2+12x=p^6+p^3+3p^3.(x-2)

Put p^3=2 ,p^6=4
x^3–8–6x^2+12x=4+2+3×2×(x-2)
x^3–6x^2+12x=8+6+6x-12
x^3–6x^2+12x-6x=14–12
x^3–6x^2+6x=2 , answer.

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