163 1.6 Other Types of Equations and Applications EXAMPLE 9 Solving an Equation Quadratic in Form Solve 12x4 - 11x2 + 2 = 0. SOLUTION 12x4 - 11x2 + 2 = 0 121x222 - 11x2 + 2 = 0 x4 = 1x222 12u2 - 11u + 2 = 0 Let u = x2. Then u2 = x4. 13u - 2214u - 12 = 0 Solve the quadratic equation. 3u - 2 = 0 or 4u - 1 = 0 Zero-factor property u = 2 3 or u = 1 4 Solve each equation. x2 = 2 3 or x2 = 1 4 Replace u with x2. x = {B2 3 or x = {B1 4 Square root property x = {22 23 # 23 23 or x = { 1 2 Simplify radicals. x = { 26 3 Check that the solution set is E { 26 3 , { 1 2F. S Now Try Exercise 87. 1.6 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. A(n) is an equation that has a rational expression for one or more terms. 2. Proposed solutions for which any denominator equals are excluded from the solution set of a rational equation. 3. If a job can be completed in 4 hr, then the rate of work is of the job per hour. 4. When the power property is used to solve an equation, it is essential to check all proposed solutions in the . 5. An equation such as x3/2 = 8 is an equation with a(n) , because it contains a variable raised to an exponent that is a rational number. NOTE To solve the equation from Example 9, 12x4 - 11x2 + 2 = 0, we could factor 12x4 - 11x2 + 2 directly as 13x2 - 2214x2 - 12, set each factor equal to 0, and then solve the resulting two quadratic equations. Which method to use is a matter of personal preference.
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