Solve for x x^4-8x^2+7=0

Problem

x4−8*x2+7=0

Solution

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

u2−8*u+7=0

2. Factor the quadratic equation by finding two numbers that multiply to 7 and add to −8

(u−7)*(u−1)=0

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

u=7

u=1

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

x2=7

x2=1

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

x=±√(,7)

x=±1

Final Answer

x=±1,±√(,7)

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