ax^{2}+bx+c = 0
2ax+b = ( b^{2}+(-4)·ac )^{(1/2)}
(12) >] 1
ax^{2}+bx+c = ...
... a·(x+( 1/(2a) )·( b+(-1)·( b^{2}+(-4)·ac )^{(1/2)} ))·...
... (x+( 1/(2a) )·( b+( b^{2}+(-4)·ac )^{(1/2)} ))
| 1 | a+b | ab |
| 1 | b | ab+(-1)·ab = 0 |
x^{2}+(a+b)·x+ab = (x+a)·(x+b)
| 1 | a+b | ab |
| 1 | a | ab+(-1)·ab = 0 |
x^{2}+(a+b)·x+ab = (x+b)·(x+a)
ax^{3}+bx^{2}+cx+d = 0
x = ( y+(-1)·(1/3)·(b/a) )
y^{3}+py+q = 0
y = u+v
( u^{3}+v^{3} = (-q) & 3uv·y = (-1)·p·y )
(uv)^{3} = (-1)^{3}·(1/27)·p^{3}
(vu)^{3} = (-1)^{3}·(1/27)·p^{3}
u^{6}+(vu)^{3} = (-q)·u^{3}
(uv)^{3}+v^{6} = (-q)·v^{3}
u^{6}+(-1)^{3}·(1/27)·p^{3} = (-q)·u^{3}
v^{6}+(-1)^{3}·(1/27)·p^{3} = (-q)·v^{3}
(123) >] (13) >] 3 [< (12) >] 1
| 1 | 0 | p | q |
| 1 | s | p+h^{2} | q+ph+h^{3} = 0 |
y^{3}+py+q = (y+(-h))·( y^{2}+hy+(p+h^{2}) )
y^{3}+py+q = y^{3}+( hy^{2}+(-h)·y^{2} )+py+( h^{2}y+(-1)·h^{2}y )+(-1)·( ph+h^{3} )
p = (-1)·(1/3)·(b/a)^{2}+(c/a)
q = (2/27)·(b/a)^{3}+(-1)·(1/3)·(b/a)·(c/a)+(d/a)
ax^{3}+bx^{2}+cx+d = ...
... a·(x+( (1/3)·(b/a)+(-h) ))·( ( x+(1/3)·(b/a) )^{2}+h·( x+(1/3)·(b/a) )+(p+h^{2}) )
| 1 | a+b+c | ab+bc+ca | abc |
| 1 | a+b | ab | abc+(-1)·abc = 0 |
x^{3}+(a+b+c)·x^{2}+(ab+bc+ca)·x+abc = (x+c)·( x^{2}+(a+b)·x+ab )
x^{3}+x^{2}+x+1 = 0
y = ( x+(-1)·(1/3) )
y^{3}+py+q = 0
p = (2/3)
q = (20/27)
h = (1/3)·( (1/2)·( (-20)+432^{(1/2)} ) )^{(1/3)}+...
... (1/3)·( (1/2)·( (-20)+(-1)·432^{(1/2)} ) )^{(1/3)}
h = (-1)·(2/3)
h^{3} = ((-8)/27)
(-q)+(-p)·h = h^{3}
((-20)/27)+((-2)/3)·((-2)/3) = ((-8)/27)
x_{0} = h+(-1)·(1/3) = (-1)
x^{3}+x^{2}+x+1 = (x+1)·(x^{2}+1) = (x+1)·(x+(-i))·(x+i)
To be:
Present:
I ame
yu its
he is
she is
wies somitch
yues sowitch
hies are
shies are
Pasat:
I weme
yu wots
he wos
she wos
wies foremitch
yues forewitch
hies were
shies were
Pasat imperfect:
I same
yu sots
he sos
she sos
wies eremitch
yues erewitch
hies sare
shies sare
I me vare-kate pust off the jaked,
becose sos making hot.
I me vare-kate pust on the jaked,
becose sos making frost.
put [o] putear
pust [o] poner
pust on [o] poner-se
pust off [o] des-poner-se
wish [o] desear
switch [o] pulsar
switch on [o] encender
switch off [o] des-encender
stanke [o] estancar
take [o] tomar
take on [o] aterrizar
take off [o] des-aterrizar
If I huviese-kate gowed to the bar,
I shut ame taking a coffi in the bar.
I not havere-kate gowed to the bar,
and I ame not taking a coffi in the bar.
If hies huviese-kate hafed milk in the bar,
I shut havere-kate taked a coffi wizh milk in the bar.
Hies not havere-kate hafed milk in the bar,
and I not havere-kate taked a coffi wizh milk in the bar.
Teorema:
Si ( [Ec][ f(x) es continua a x = c ] & f(x+y) = f(x)+f(y) ) ==> [Ax][ f(x) es continua ]
Demostración:
| f(h) | = | f(c+h+(-c)) | = | f(c+h)+(-1)·f(c) | < s
| f(x+h)+(-1)·f(x) | = | f(x+h+(-x)) | = | f(h) | < s
Teorema:
Si f(x+y) = f(x)+y ==> [Ax][ f(x) es continua ]
Demostración:
| f(x+h)+(-1)·f(x) | = | f(x)+h+(-1)·f(x) | = |h| < s
