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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Answer to a math 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
Eliseo
4.6111 Answers
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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