Melchor Bernabé Gustavo. Semana 8
Resolución de Ecuaciones Cuadráticas y Sistemas
6x^2=0
x^2=0
x=0
Solución.- x=0
x^2-25=0
x^2=25
x=±5
Solución.- x=5
x=-5
9x^2-1=0
9x^2=1
x^2= 1/9
x^2= ± 1/3
Solución.-x= 1/3
x=-1/3
Sistema 1
x - y - z = 0
x + 2y - 5z = 2
3x - 2y - 4z = 1
x = y + z
(y + z) + 2y - 5z = 2
y + z + 2y - 5z = 2
3y - 4z = 2
3(y + z) - 2y - 4z = 1
3y + 3z - 2y - 4z = 1
y - z = 1
3y - 4z = 2
2y - 2z = 2
y = z + 1
3(z + 1) - 4z = 2
3z + 3 - 4z = 2
-z = -1
z = 1
y = 1 + 1 = 2
x = y + z = 2 + 1 = 3
(3, 2, 1)
Sistema 2
x + z = y
a) 2(x + z) - 3(y - 1)
2(y + z) = 3(1 - x - z)
2(x + z) - 3(y - 1)
2x + 2z - 3y + 3 = 0
-x - z + 3y - 3 = 0 → x + z = 3y - 3
2(y + z) = 3(1 - x - z)
2y + 2z = 3 - 3x - 3z
2y + 2z = 3 - 3x - 3z
5x + y + 7z = 3
5x + y + 7z = 3
x + z = 3y - 3 → Sust. x = 3y - 3 - z
5(3y - 3 - z) + y + 7z = 3
15y - 15 - 5z + y + 7z = 3
16y - 15 + 2z = 3 → z = -4
Sust. z = -4
x + z = 1 → x = 2
Fin. x = 2, z = -4 y x + z = 1 → y = 1
(x, y, z) = (2, 1, -4)