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By Macrobert Thomas M
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136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. Solving Equations 27 ԽxԽ ϭ x 2 ϩ x Ϫ 3 Խx 2 ϩ 6xԽ ϭ 3x ϩ 18 Խx ϩ 1Խ ϭ x 2 Ϫ 5 Խx Ϫ 10Խ ϭ x 2 Ϫ 10x ANTHROPOLOGY In Exercises 155 and 156, use the following information. 15 Male where y is the length of the femur in inches and x is the height of the adult in inches (see figure). Ί2x Ϫ 10 ϭ 0 7Ίx Ϫ 6 ϭ 0 Ίx Ϫ 10 Ϫ 4 ϭ 0 Ί5 Ϫ x Ϫ 3 ϭ 0 Ί2x ϩ 5 ϩ 3 ϭ 0 Ί3 Ϫ 2x Ϫ 2 ϭ 0 3 2x ϩ 1 ϩ 8 ϭ 0 Ί 3 4x Ϫ 3 ϩ 2 ϭ 0 Ί Ί5x Ϫ 26 ϩ 4 ϭ x Ίx ϩ 5 ϭ Ί2x Ϫ 5 ͑x Ϫ 6͒3͞2 ϭ 8 ͑x ϩ 3͒3͞2 ϭ 8 ͑x ϩ 3͒2͞3 ϭ 5 ͑x2 Ϫ x Ϫ 22͒4͞3 ϭ 16 3x͑x Ϫ 1͒1͞2 ϩ 2͑x Ϫ 1͒3͞2 ϭ 0 4x2͑x Ϫ 1͒1͞3 ϩ 6x͑x Ϫ 1͒4͞3 ϭ 0 3 1 xϭ ϩ x 2 4 3 Ϫ ϭ1 xϩ1 xϩ2 20 Ϫ x ϭx x 3 4x ϩ 1 ϭ x 1 x ϩ ϭ3 x2 Ϫ 4 x ϩ 2 xϩ1 xϩ1 Ϫ ϭ0 3 xϩ2 Խ2x Ϫ 1Խ ϭ 5 Խ13x ϩ 1Խ ϭ 12 x in.
4x ϩ 4 Square each side. 0 ϭ x 2 ϩ 2x Ϫ 3 Write in general form. 0 ϭ ͑x ϩ 3͒͑x Ϫ 1͒ Factor. xϩ3ϭ0 x ϭ Ϫ3 Set 1st factor equal to 0. xϪ1ϭ0 xϭ1 Set 2nd factor equal to 0. By checking these values, you can determine that the only solution is x ϭ 1. b. Ί2x Ϫ 5 Ϫ Ίx Ϫ 3 ϭ 1 Original equation Ί2x Ϫ 5 ϭ Ίx Ϫ 3 ϩ 1 2x Ϫ 5 ϭ x Ϫ 3 ϩ 2Ίx Ϫ 3 ϩ 1 Square each side. 2x Ϫ 5 ϭ x Ϫ 2 ϩ 2Ίx Ϫ 3 Combine like terms. x Ϫ 3 ϭ 2Ίx Ϫ 3 When an equation contains two radicals, it may not be possible to isolate both. In such cases, you may have to raise each side of the equation to a power at two different stages in the solution, as shown in Example 12(b).
91. 92. 93. 94. 95. 96. 97. 98. 25x 2 Ϫ 20x ϩ 3 ϭ 0 2 ϩ 2x Ϫ x 2 ϭ 0 x 2 Ϫ 10x ϩ 22 ϭ 0 x 2 ϩ 14x ϩ 44 ϭ 0 6x ϭ 4 Ϫ x 2 x 2 ϩ 8x Ϫ 4 ϭ 0 4x 2 Ϫ 4x Ϫ 4 ϭ 0 12x Ϫ 9x 2 ϭ Ϫ3 16x 2 ϩ 22 ϭ 40x 9x2 ϩ 24x ϩ 16 ϭ 0 16x 2 Ϫ 40x ϩ 5 ϭ 0 28x Ϫ 49x 2 ϭ 4 3x ϩ x 2 Ϫ 1 ϭ 0 8t ϭ 5 ϩ 2t 2 25h2 ϩ 80h ϩ 61 ϭ 0 ͑ y Ϫ 5͒2 ϭ 2y ͑57x Ϫ 14͒2 ϭ 8x In Exercises 99–104, use the Quadratic Formula to solve the equation. ) 99. 100. 101. 102. 103. 104. 651 ϭ 0 In Exercises 105–112, solve the equation using any convenient method.