Find the solution of the equation x4 2x3 - 2r2 2x +1 0.

1.	Find the solution of the equation x4 2x3 - 2r2 2x +1 0.
Answer» x^4–2x^3+2x^2–2x+1=0 divide both side by x^2. x^2–2x+3–2/x+1/x^2=0 x^2+1/x^2–2(x+1/x)+3=0 x^2+2+1/x^2–2(x+1/x)+1=0 (x+1/x)^2–2(x+1/x)+1=0 Let x+1/x=t t^2–2t+1=0 (t-1)^2=0 t-1=0 t=1 , put t=x+1/x x+1/x=1 or x^2+1=x or x^2-x+1=0 or (x)^2–2×x×1/2+(1/2)^2+1–1/4=0 or (x-1/2)^2=-3/4=(3i^2)/4=3(i/2)^2. or x-1/2=+/-3^1/2.(i/2) or x=1/2+/-3^1/2.(i/2). or x=(1+/-i.3^1/2)/2

Answer»

x^4–2x^3+2x^2–2x+1=0

divide both side by x^2.

x^2–2x+3–2/x+1/x^2=0

x^2+1/x^2–2(x+1/x)+3=0

x^2+2+1/x^2–2(x+1/x)+1=0

(x+1/x)^2–2(x+1/x)+1=0

Let x+1/x=t

t^2–2t+1=0

(t-1)^2=0

t-1=0

t=1 , put t=x+1/x

x+1/x=1

or x^2+1=x

or x^2-x+1=0

or (x)^2–2×x×1/2+(1/2)^2+1–1/4=0

or (x-1/2)^2=-3/4=(3i^2)/4=3(i/2)^2.

or x-1/2=+/-3^1/2.(i/2)

or x=1/2+/-3^1/2.(i/2).

or x=(1+/-i.3^1/2)/2

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