EXAMPLE 3 Solve. a) x4 10x2 9 0 b) t2/3 t1/3 6 0 Solution a) Let’s compare x4 10x2 9 0 to x2 10x 9 0. We can factor x2 10x 9: (x 9)(x 1) Confi rm by multiplying using FOIL: (x 9)(x 1) x2 x 9x 9 x2 10x 9 We can solve x4 10x2 9 0 by factoring. x4 10x2 9 0 (x2 9)(x2 1) 0 Factor. b R The check is left to the student. Check the answers in the original equation. The solution set is 53, 1, 1, 36. b) Compare t x2 9 0 or x2 1 0 Set each factor equal to 0. x2 9 x2 1 Square root property x 3 x 1 2/3 t 1/3 6 0 to t Factor x4 10x2 9 in a similar way since the exponent, 4, of the fi rst term is twice the exponent, 2, of the second term: x4 10x2 9 (x2 9)(x2 1) Confi rm by multiplying using FOIL: (x2 9)(x2 1) x4 x2 9x2 9 2 t 6 0. We can factor t 2 t 6: (t 3)(t 2) Confi rm by multiplying using FOIL: (t 3)(t 2) t 2 2t 3t 6 t 2 t 6 x4 10x2 9 Factor t 2/3 t1/3 6 in a similar way since the exponent, 2 3 , of the fi rst term is twice the exponent, 1 3 , of the second term: t 2/3 t1/3 6 (t1/3 3)(t1/3 2) Confi rm by multiplying using FOIL: (t1/3 3)(t1/3 2) t 2/3 2t1/3 3t1/3 6 t 2/3 t1/3 6 We can solve t2/3 t1/3 6 0 by factoring. t 23 t13 6 0 (t 13 3)(t13 2) 0 Factor. b R t13 3 0 or t13 2 0 Set each factor equal to 0. t13 3 t13 2 Isolate the constant. 1 3 t 3 1 3 t 2 t13 1 3 t (1 3 t)3 (3)3 (1 3 t)3 23 Cube both sides. t 27 or t 8 Solve. The check is left to the student. The solution set is {27, 8}. Be sure you understand why you are performing each step as you are writing out the examples. www.mhhe.com/messersmith SECTION 10.3 Equations in Quadratic Form 639
messersmith_power_intermediate_algebra_1e_ch4_7_10
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