Solve for x x^4-10x^2+9=0

Problem

x4−10*x2+9=0

Solution

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

u2−10*u+9=0

2. Factor the quadratic equation by finding two numbers that multiply to 9 and add to −10

(u−9)*(u−1)=0

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

u=9

u=1

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

x2=9

x2=1

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

x=±3

x=±1

Final Answer

x={−3,−1,1,3}

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