Respuestas sección 4.1

Ejercicios 1 al 10. Método de evaluación para obtener los ceros de los siguientes polinomios.

  1. (x+1)(x−2)(x−3)(x2+3x+4)\hspace{0.1cm}\left(x+1\right)\left(x-2\right)\left(x-3\right)\left(x^2+3x+4\right)\\[0.2cm]
  2. (x+2)(x−3)(x+4)(3x+2)(2x−1)\hspace{0.1cm}\left(x+2\right)\left(x-3\right)\left(x+4\right)\left(3x+2\right)\left(2x-1\right)\\[0.2cm]
  3. (x−2)(x−3)(x+3)\hspace{0.1cm}\left(x-2\right)\left(x-3\right)\left(x+3\right)\\[0.2cm]
  4. (x+1)2(x+2)(x−4)\hspace{0.1cm}\left(x+1\right)^2\left(x+2\right)\left(x-4\right)\\[0.2cm]
  5. (a+5)(a−4)(a+1)(a−2)(a−3)(a+3)\hspace{0.1cm}\left(a+5\right)\left(a-4\right)\left(a+1\right)\left(a-2\right)\left(a-3\right)\left(a+3\right)\\[0.2cm]
  1. (a3−2)(a−2)(a+2)(a−4)(a+4)\hspace{0.1cm}\left(a^3-2\right)\left(a-2\right)\left(a+2\right)\left(a-4\right)\left(a+4\right)\\[0.2cm]
  2. (x−2)2(x+1)(x−1)\hspace{0.1cm}\left(x-2\right)^2\left(x+1\right)\left(x-1\right)\\[0.2cm]
  3. (x−4)(x+3)(x−2)(x+1)\hspace{0.1cm}\left(x-4\right)\left(x+3\right)\left(x-2\right)\left(x+1\right)\\[0.2cm]
  4. (n−5)(n+4)(n−2)(n+3)\hspace{0.1cm}\left(n-5\right)\left(n+4\right)\left(n-2\right)\left(n+3\right)\\[0.2cm]
  5. (3x+5)(5x−2)(x−1)(x+6)\hspace{0.1cm}\left(3x+5\right)\left(5x-2\right)\left(x-1\right)\left(x+6\right)\\[0.2cm]

Respuesta a los ejercicios 11 y 20. Ecuaciones exponenciales.

  1. x=log  (281)log  (24)≈−1.16\hspace{0.1cm}x=\frac{log\;\left(\frac{2}{81}\right)}{log\;\left(24\right)}\approx -1.16\\[0.2cm]
  2. x=−log  (200)log  (45)≈23.744\hspace{0.1cm}x=-\frac{log\;\left(200\right)}{log\;\left(\frac{4}{5}\right)}\approx 23.744\\[0.2cm]
  3. x=−log  (1600)log  (165)≈−6.343\hspace{0.1cm}x=-\frac{log\;\left(1600\right)}{log\;\left(\frac{16}{5}\right)}\approx -6.343\\[0.2cm]
  4. x=−log  (5308416)log  (32)≈−38.19\hspace{0.1cm}x=-\frac{log\;\left(5308416\right)}{log\;\left(\frac{3}{2}\right)}\approx -38.19\\[0.2cm]
  5. x=−2\hspace{0.1cm}x=-2\\[0.2cm]
  1. x=3\hspace{0.1cm}x=3\\[0.2cm]
  2. x=114\hspace{0.1cm}x=\frac{11}{4}\\[0.2cm]
  3. x=−3\hspace{0.1cm}x=-3\\[0.2cm]
  4. x=2\hspace{0.1cm}x=2\\[0.2cm]
  5. x=−4\hspace{0.1cm}x=-4\\[0.2cm]

Ejercicios 21 y 30. Ecuaciones logaritmicas.

  1. x=7\hspace{0.1cm}x=7\\[0.2cm]
  2. x=2\hspace{0.1cm}x=2\\[0.2cm]
  3. x=72\hspace{0.1cm}x=\frac{7}{2}\\[0.2cm]
  4. x=±8\hspace{0.1cm}x=\pm 8\\[0.2cm]
  5. x=32\hspace{0.1cm}x=\frac{3}{2}\\[0.2cm]
  1. x=20∧y=2\hspace{0.1cm}x=20\wedge y=2\\[0.2cm]
  2. x=10∧y=1\hspace{0.1cm}x=10\wedge y=1\\[0.2cm]
  3. x=100∧y=10\hspace{0.1cm}x=100\wedge y=10\\[0.2cm]
  4. x=100∧y=10−1\hspace{0.1cm}x=100\wedge y=10^{-1}\\[0.2cm]
  5. x=100∧y=10\hspace{0.1cm}x=100\wedge y=10\\[0.2cm]

Ejercicios 31 y 40. Problemas de aplicación.

  1. 3∧13\hspace{0.1cm}3 \wedge \cfrac{1}{3}
  2. 10∧15\hspace{0.1cm}10\wedge 15
  3. 85\hspace{0.1cm}85
  4. 30m.×60m.\hspace{0.1cm}30m. \times 60m.
  5. \hspace{0.1cm}45 años y 9 años
  1. (373−21)  \hspace{0.1cm}\left(3\sqrt{73}-21\right)\;metros
  2. 152∧32\hspace{0.1cm}\cfrac{15}{2}\wedge \cfrac{3}{2}
  3. \hspace{0.1cm}1.3 cm.
  4. \hspace{0.1cm}50 galones del primer tanque y 40galones del segundo tanque.
  5. \hspace{0.1cm}A=4,B=2,C=5 Horas respectivamente