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

Problem

x4−4*x2+3=0

Solution

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

u2−4*u+3=0

2. Factor the quadratic equation by finding two numbers that multiply to 3 and add to −4

(u−1)*(u−3)=0

3. Solve for u by setting each factor equal to zero.

u=1

u=3

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

x2=1

x2=3

5. Apply the square root property to solve for x in both equations.

x=±√(,1)

x=±√(,3)

6. Simplify the results to obtain the final set of solutions.

x=1,−1,√(,3),−√(,3)

Final Answer

x=±1,±√(,3)

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