Ejercicio 111 – Solucionario Baldor

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DESCARGA

CAPITULO XI

Máximo común divisor de monomios m.c.d

Ejercicio 111

Hallar el m.c.d de:

$a^{2} x, a x^{2}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n 1, e n a m b o s t é r m i n o s y l a s l e t r a s a, x c o n e x p o n e n t e s m í n i m o s 1 \\ m . c . d & = a x \end{matrix}$
$a b^{2} c, a^{2} b c$
$\begin{matrix} L o s c o e f i c i e n t e s s o n 1, e n a m b o s t é r m i n o s y l a s l e t r a s a, b, c c o n e x p o n e n t e s m í n i m o s 1 \\ m . c . d = & a b c \end{matrix}$
$2 x^{2} y, x^{2} y^{3}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (1, 2) y l a s l e t r a s x, y c o n e x p o n e n t e s m í n i m o s x = 2, y = 1 \\ m . c . d & = x^{2} y \end{matrix}$
$6 a^{2} b^{3}, 15 a^{3} b^{4}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (6, 15) = (2.3, 3.5) y l a s l e t r a s a, b c o n e x p o n e n t e s m í n i m o s a = 2, b = 3 \\ m . c . d & = 3 a^{2} b^{3} \end{matrix}$
$8 a m^{3} n, 20 x^{2} m^{2}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (8, 20) = (2^{3}, 2^{2} .5) y l a l e t r a m c o n e x p o n e n t e m í n i m o m = 2 \\ m . c . d & = 4 m^{2} \end{matrix}$
$18 m n^{2}, 27 a^{2} m^{3} n^{4}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (18, 27) = (2. 3^{2}, 3^{3}) y l a s l e t r a s m, n c o n e x p o n e n t e s m í n i m o s m = 1, n = 2 \\ m . c . d & = 9 m n^{2} \end{matrix}$
$15 a^{2} b^{3} c, 24 a b^{2} x, 36 b^{4} x^{2}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (15, 24, 36) = (3.5, 3. 2^{3}, 3^{2} . 2^{2}) y l a l e t r a b c o n e x p o n e n t e m í n i m o b = 2 \\ m . c . d & = 3 b^{2} \end{matrix}$
$12 x^{2} y z^{3}, 18 x y^{2} z, 24 x^{3} y z^{2}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (12, 18, 24) = (3. 2^{2}, 2. 3^{2}, 2.3.4) y l a s l e t r a s x, y, z c o n e x p o n e n t e s m í n i m o s x = 1, y = 1, z = 1 \\ m . c . d & = 2.3 x y z \\ = 6 x y z \end{matrix}$
$28 a^{2} b^{3} c^{4}, 35 a^{3} b^{4} c^{5}, 42 a^{4} b^{5} c^{6}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (28, 35, 42) = (7. 2^{2}, 7.5, 7.6) y l a s l e t r a s a, b, c c o n e x p o n e n t e s m í n i m o s a = 2, b = 3, c = 4 \\ m . c . d & = 7 a^{2} b^{3} c^{4} \end{matrix}$
$72 x^{3} y^{4} z^{4}, 96 x^{2} y^{2} z^{3}, 120 x^{4} y^{5} z^{7}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (72, 96, 120) = (8. 3^{2}, 8.3.4, 8.3.4) y l a s l e t r a s x, y, z c o n e x p o n e n t e s m í n i m o s x = 2, y = 2, z = 3 \\ m . c . d & = 8.3 x^{2} y^{2} z^{3} \\ = 24 x^{2} y^{2} z^{3} \end{matrix}$
$42 a m^{2} n, 56 m^{3} n^{2} x, 70 m^{4} n^{2} y$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (42, 56, 70) = (14.3, 14.4, 14.5) y l a s l e t r a s m, n c o n e x p o n e n t e s m í n i m o s m = 2, n = 1 \\ m . c . d & = 14 m^{2} n \end{matrix}$
$75 a^{4} b^{3} c^{2}, 150 a^{5} b^{7} x^{2}, 225 a^{3} b^{6} y^{2}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (75, 150, 225) = (15.5, 15.5.2, 15.5.3) y l a s l e t r a s a, b c o n e x p o n e n t e s m í n i m o s a = 3, b = 3 \\ m . c . d & = 15.5 a^{3} b^{3} \\ = 75 a^{3} b^{3} \end{matrix}$
$4 a^{2} b, 8 a^{3} b^{2}, 2 a^{2} b c, 10 a b^{3} c^{2}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (4, 8, 2, 10) = (2^{2}, 2^{3}, 2, 2.5) y l a s l e t r a s a, b c o n e x p o n e n t e s m í n i m o s a = 1, b = 1 \\ m . c . d & = 2 a b \end{matrix}$
$38 a^{2} x^{6} y^{4}, 76 m x^{4} y^{7}, 95 x^{5} y^{6}$
$\begin{matrix} L o s c o e f i c i e n t e s s o n (38, 76, 95) = (19.2, 19.4, 19.5) y l a s l e t r a s x, y c o n e x p o n e n t e s m í n i m o s x = 4, y = 4 \\ m . c . d & = 19 x^{4} y^{4} \end{matrix}$