Ejercicio 272 – Solucionario Baldor

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DESCARGA

CAPITULO XXXIII

Ecuaciones incompletas de segundo grado

Ejercicio 272

Resolver las ecuaciones:

$\begin{matrix} x^{2} & = 5 x \\ x^{2} - 5 x & = 0 \\ x (x - 5) & = 0 \\ x_{1} & = 0 \\ x - 5 & = 0 \\ x_{2} & = 5 \end{matrix}$
$\begin{matrix} 4 x^{2} & = - 32 x \\ 4 x^{2} + 32 x & = 0 \\ 4 x (x + 8) & = 0 \\ 4 x & = 0 \\ x_{1} & = 0 \\ x + 8 & = 0 \\ x_{2} & = - 8 \end{matrix}$
$\begin{matrix} x^{2} - 3 x & = 3 x^{2} - 4 x \\ x^{2} - 3 x^{2} + 4 x - 3 x & = 0 \\ - 2 x^{2} + x & = 0 \\ x (- 2 x + 1) & = 0 \\ x_{1} & = 0 \\ - 2 x + 1 & = 0 \\ - 2 x & = - 1 \\ x_{2} & = \frac{1}{2} \end{matrix}$
$\begin{matrix} 5 x^{2} + 4 & = 2 (x + 2) \\ 5 x^{2} + 4 & = 2 x + 4 \\ 5 x^{2} - 2 x & = 0 \\ x (5 x - 2) & = 0 \\ x_{1} & = 0 \\ 5 x - 2 & = 0 \\ 5 x & = 2 \\ x_{2} & = \frac{2}{5} \end{matrix}$
$\begin{matrix} {(x - 3)}^{2} - {(2 x + 5)}^{2} & = - 16 \\ x^{2} - 6 x + 9 - (4 x^{2} + 20 x + 25) & = - 16 \\ x^{2} - 6 x + 9 - 4 x^{2} - 20 x - 25 & = - 16 \\ - 3 x^{2} - 26 x - 16 & = 16 \\ 3 x^{2} + 26 x & = 0 \\ x (3 x + 26) & = 0 \\ x_{1} & = 0 \\ 3 x + 26 & = 0 \\ 3 x & = - 26 \\ x_{2} & = - \frac{26}{3} \end{matrix}$
$\begin{matrix} \frac{x^{2}}{3} - \frac{x - 9}{6} & = \frac{3}{2} \\ M u l t i p l i c a n d o l a e c u a c i ó n p o r 6 \\ 2 x^{2} - x + 9 & = 9 \\ x (2 x - 1) & = 0 \\ x_{1} & = 0 \\ 2 x - 1 & = 0 \\ 2 x & = 1 \\ x_{2} & = \frac{1}{2} \end{matrix}$
$\begin{matrix} (4 x - 1) (2 x + 3) & = (x + 3) (x - 1) \\ 8 x^{2} + 12 x - 2 x - 3 & = x^{2} + 2 x - 3 \\ 8 x^{2} + 10 x - x^{2} - 2 x & = 0 \\ 7 x^{2} + 8 x & = 0 \\ x (7 x + 8) & = 0 \\ x_{1} & = 0 \\ 7 x + 8 & = 0 \\ 7 x & = - 8 \\ x_{2} & = - \frac{8}{7} \end{matrix}$
$\begin{matrix} \frac{x + 1}{x - 1} - \frac{x + 4}{x - 2} & = 1 \\ \frac{(x + 1) (x - 2) - (x + 4) (x - 1)}{(x - 1) (x - 2)} & = 1 \\ x^{2} - x - 2 - (x^{2} + 3 x - 4) & = (x - 1) (x - 2) \\ x^{2} - x - 2 - x^{2} - 3 x + 4 & = x^{2} - 3 x + 2 \\ 0 & = x^{2} + x + 2 - 2 \\ 0 & = x (x + 1) \\ x_{1} & = 0 \\ 0 & = x + 1 \\ x_{2} & = - 1 \end{matrix}$