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

Problem

x4−3*x2+2=0

Solution

1. Substitute a new variable to transform the equation into a quadratic form. Let u=x2

2. Rewrite the original equation in terms of u

u2−3*u+2=0

3. Factor the quadratic equation by finding two numbers that multiply to 2 and add to −3

(u−1)*(u−2)=0

4. Solve for u by setting each factor to zero.

u=1

u=2

5. Back-substitute x2 for u to find the values of x

x2=1

x2=2

6. Extract the square roots to find all possible solutions for x

x=±√(,1)

x=±√(,2)

Final Answer

x=1,−1,√(,2),−√(,2)

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