Question

X^4-10x^2+9=0 1. Factor the expression. State your factors 2. State the solutions to the equation. If necessary use “sqrt” for radicals; do NOT provide a decimal approximation

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Eliseo

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1. Start with the equation:

X^4 - 10x^2 + 9 = 0

2. Let \(Y = X^2\). Then the equation becomes:

Y^2 - 10Y + 9 = 0

3. Solve the quadratic equation by factoring:

(Y - 1)(Y - 9) = 0

4. Substitute back \(Y = X^2\):

(X^2 - 1)(X^2 - 9) = 0

5. Factor each term:

(X - 1)(X + 1)(X - 3)(X + 3) = 0

6. Set each factor equal to zero and solve for \(X\):

X - 1 = 0 \Rightarrow X = 1

X + 1 = 0 \Rightarrow X = -1

X - 3 = 0 \Rightarrow X = 3

X + 3 = 0 \Rightarrow X = -3

Answer:

\text{Factors:} \ (X^2 - 1)(X^2 - 9) = (X - 1)(X + 1)(X - 3)(X + 3)

\text{Solutions:} \ X = \pm 1, \pm 3

2. Let \(Y = X^2\). Then the equation becomes:

3. Solve the quadratic equation by factoring:

4. Substitute back \(Y = X^2\):

5. Factor each term:

6. Set each factor equal to zero and solve for \(X\):

Answer:

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