Find the solution set of the equation by introducing a substitution. 81x⁴ - 18x² + 1 = 0 A) {-1/9, 1/9} B) {1/9} C) {-1/3,1/3} D) {1/3}

Name: Find the solution set of the equation by introducing a substitution. 81x 4 - 18x 2 + 1 = 0 A) {-1/9, 1/9} B) {1/9} C) {-1/3,1/3} D) {1/3}
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Question

Quizplus · Accepted Answer

By substituting y = x^2, the equation becomes 81y^2 - 18y + 1 = 0. Solving this quadratic equation gives y = 1/9. Since y = x^2, x = ±√(1/9) = ±1/3. Thus, the solution set is {-1/3, 1/3}.

Find the Solution Set of the Equation by Introducing a Substitution