Solve by Factoring x^4-6x^2+5=0

Problem

x4−6*x2+5=0

Solution

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

u2−6*u+5=0

2. Factor the quadratic expression by finding two numbers that multiply to 5 and add to −6

(u−5)*(u−1)=0

3. Substitute back the original variable x2 in place of u

(x2−5)*(x2−1)=0

4. Factor further using the difference of squares for the term (x2−1)

(x2−5)*(x−1)*(x+1)=0

5. Set each factor to zero to solve for x

x2−5=0⇒x2=5⇒x=±√(,5)

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x=√(,5),−√(,5),1,−1

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