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Transcript of άλγεβρα 1ης...

• : : 2 : 1

• - = + (-)

(0)

+ = + = + ( + ) = ( + ) + ()=() + 0 = 1 = / + (-) = 0 = 1, 0 ( + ) = +

• 2( = = ) + = + ( = = ) = = + = + 0 , : = = = 0 = 0 = 0 0 0 0

• , : = > 1 1 = , = 1

0, :0 = 1 - =

• 1. = + 2. = - 3. = () 4. 5. () =

( 0 )

• ( + )2 = 2 + 2 + 2( - )2 = 2 - 2 + 2 2 - 2 = ( + ) ( - ) ( + )3 = 3 + 32 + 32 + 3 ( - )3 = 3 - 32 + 32 - 3 3 + 3 = ( + ) (2 + 2)3 - 3 = ( - ) (2 + + 2)( + + )2 = 2 + 2 + 2 + 2 + 2 + 2

• 29. 2 + 2 = ( + )2 - 210. ( + - )2 = 2 + 2 + 2 + 2 - 2 - 211. = ( - ) (-1 + -2 + + -2 + -1) 12. 3 + 3 +3 3 = (++) (2+2+2---)13. 3+3+3 3 = (++)[(-)2+(-)2+(-)2]14. + + = 0 3 + 3 + 3 = 315. = = 3 + 3 + 3 = 316. 3 + 3 = ( + )3 - 3 ( + )

• ( 0) ( 0) ( 0) ( (+) 0)

• > , - 1. ( > 0 > 0) + > 0 ( < 0 < 0) + < 02. , > 0 , < 0

• 3. 2 0, , ( =0) :2 + 2 = 0 = 0 = 02 + 2 > 0 0 0

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• ( > > ) > i. > + > + ii. > 0, : > > iii. < 0, : > < i.( > > ) + > + ii. , , , : ( > > ) > , : > >

• , 0 -, 0) x = -

• = ( 0) d ( , ) =

x >

• , , . 0, x2 = .

0 & 0, :

( 0 )

• - , , . 0, x = .

• , 0, : ( 0) 0, : 0 & , :

• > 0, & ,

, :

• x = x = , > 0 , , : x = , > 0 , : x = , < 0 , , : x = , < 0 ,

• x2+x+=0, 0 x2 + x + = 0 , 0 .

= 2 - 4 x2 + x + = 0 , 0 > 0 = 0 < 0

• x1 , x2 :x2 Sx + P = 0

• 1 x + > 0 > 0 , :

< 0 , : = 0 , : , x , > 0 , 0

• 2 x2 + x + = 0 , 0 2 . x2 + x + = 0 , 0 : > 0 , : = 0 , : < 0 ,:

• x2 + x + = 0 , 0

> 0 - x1 x2 + = 0 - x1 + < 0 - + x

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