Find all solutions of x^4 - 3x^2 + 2 = 0?

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We have to find all the solutions of x^4 - 3x^2 + 2 = 0.

Now let y = x^2

x^4 - 3x^2 + 2 = 0

=> y^2 - 3y + 2 = 0

=> y^2 - 2y - y + 2 =0

=> y*(y - 2) - 1*(y - 2) =0

=> (y - 1)(y - 2) = 0

=> y = 1 or y = 2

As y = x^2

x^2 = 1

=> x = 1 or x = -1

x^2 = 2

=> x = sqrt 2 or -sqrt 2

Therefore the solutions of the equation x^4 - 3x^2 + 2 = 0 are 1, -1, sqrt 2, -sqrt 2.

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