EXAMPLE 5 Solve 2n4 5n2 1. YOU TRY 5 Solution Write the equation in standard form: 2n4 5n2 1 0. Can we solve the equation by factoring? No. We will solve 2n4 5n2 1 0 using the quadratic formula. Begin with substitution. If u n2, then u2 n4. 2n4 5n2 1 0 2u2 5u 1 0 Substitute u2 for n4 and u for n2. u (5) 2(5)2 4(2)(1) 2(2) a 2, b 5, c 1 u 5 125 8 4 5 117 4 Note that u 5 117 4 does not solve the original equation. We must solve for x using the fact that u x2. Since u 5 117 4 means u 5 117 4 or u 5 117 4 , we get u x2 u x2 5 117 4 x2 5 117 4 x2 B 5 117 4 x B 5 117 4 x Square root property 25 117 2 x 25 117 2 x 14 2 The solution set is e 25 117 2 , 25 117 2 , 25 117 2 , 25 117 2 f . Solve 2k4 3 9k2. 4 Use Substitution for a Binomial to Solve a Quadratic Equation We can use substitution to solve an equation like the one in Example 6. www.mhhe.com/messersmith SECTION 10.3 Equations in Quadratic Form 641
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