Solve for x x^4-5x^2+4=0

Problem

x4−5*x2+4=0

Solution

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

u2−5*u+4=0

2. Factor the quadratic equation by finding two numbers that multiply to 4 and add to −5

(u−1)*(u−4)=0

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

u=1

u=4

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

x2=1

x2=4

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

x=±√(,1)

x=±√(,4)

Final Answer

x=±1,±2

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