Page 17 - Guia del maestro - Algebra 4° Sec

Multiplicación algebraica

Problema 3
Si a + b + c = 0, ab + bc + ac = – 19, calcule a + b + c 4
4
4
Resolución:
Si a + b + c = 0  a + b + c = –2(ab + bc + ac)
2
2
2

2
 a + b + c = 38 –19
2
2
2 2
2
4
2
4
4
También: (a + b + c ) = 2(a + b + c )
4
4
4
2
38 = 2(a + b + c )
4
4
4
 a + b + c = 722 Rpta.: 722
Recuerda
igualdades adicionales
Identidad de gauss
2
2
2
Si a + b + c = ab + bc + ac  a = b = c
n n
n n
3
2n
n n
2n
3
2n
3
Para a, b, c   y n    Si a + b + c = a b + b c + a c  a = b = c a + b + c – 3abc = (a + b + c)
2
2
(a + b + c – ab – bc – ac)
2
2
2
Si a + b + c = 0  a = b = c = 0
2
1
3
a + b + c – 3abc = (a + b + c)
3
3
Problema 4 2
2
2
2
2
2
2
Si (a – 2) + (b – 3) + (c – 5) = 0, calcule a + b + c. (a – b) + (b – c) + (a – c) 
Resolución:
2
2
2
Si (a – 2) + (b – 3) + (c – 5) = 0 ⇒ a – 2 = b – 3 = c – 5 = 0,
a = 2 ; b = 3 ; c = 5
\ a + b + c = 10
Rpta.: 10 Resuelve problemas de regularidad, equivalencia y cambio (Álgebra)
Actividad 4
2
2
2
1 Si a + b + c = 15 y a + b + c = 17, 7 Sabiendo que:
2
2
2
halle ab + ac + bc • a + b + c = 8 • a + b + c = 34 • abc = 60
1 1 1
halle E = + +
2 Si: a b c
2
2
2
3
3
3
• a + b + c = 3 • a + b + c = 7 • a + b + c = 11
calcule abc. 8 Sean x e y reales tales que:
+
+
3xy x + y − 2 xy + xy xy = . CalculeE = x + y
−
0
3
3
2
2
2
3 Si (x + y) = 4xy, calcule . y x
y
2
y 25 +
−
4 Si x ∧ y ∈  , tales que x +− x 4 = 0 , 9 Si a + b + c = a + b + c 2 = 3 a + b + c 3 = m
+
2
3
3
2
4
halle (y – 2x) . 3 7
a 2 b 2 c 2 calcule S = (a + b – c)(b + c – a)(c + a – b).
5 Si a + b + c = 0, calcule E = + +
bc ac ab
10 Sea:
−
2
2
2
6 Si a – ab + b = bc + ac – c , halle • x = 23 • y = 3 − 2 • z =−3 3
4
4
+
a + 2 b + 2 a + 3 b + 2 abc Calcule E = xyzxyz + xyz 4 2
+
+
+
2
2
3
c 3 c 5 a + b 3 ( xy) ( xz) ( yz)
Álgebra 4 - Secundaria 15