Solve the equation x^6-4x^3+3=0
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justaguide
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We have to solve x^6 - 4x^3 + 3 = 0
Let y = x^3
x^6 - 4x^3 + 3 = 0
=> y^2 - 4y + 3 = 0
=> y^2 - 3y - y...
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giorgiana1976 | Student
The equation could be solvd using substitution technique. We'll reduce the equatin to a quadratic.
We'll note x^3 = t
t^2 - 4t + 3 = 0
We'll apply the quadratic formula:
t1 = [4+sqrt(16 - 12)]/2
t1 = (4+2)/2
t1 = 3
t2 = (4-2)/2
t2 = 1
But x^3 = t
x^3 = 3
x = 3^(1/3)
x^3 = 1
x = 1
The solutions of the equation are: {3^(1/3); 1 }.
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