w1.* *' ..;),)!,, ,_;j,..,T .Y 1))1.:.1

w1.* i ~ ..;),)!,, ,_;j,..,T 1))1.:.1

v--:JI) (y) ( -x) = -xy ~)~a+b={a+~ c_) ( b - y) ~ = b ~ - f b - f

)'

r>( -oy + \)( -oy- 9') ::::= r'<-P) d + r a;J- '1

Y) (r~- ~c) ( -JYv + ~0) ~ !'v.- ~t , ..

( ,r;;; ::: r'.;;: J

\\) ( -ar + w)(a" + wf + \9-ar)

J' ". r· 9 r ,;;: ( - ~ ) + ( l o) ·:::-{A. -r y £ (}t

,, r "' I" 'r l ( n - r Y .:= ( r ,._ J- , ... J< ( I'Jt J x !" t- r'"' t'')l ')(.{" _ r·

I" t' =- 11 ,._ __ r· y?(..,... o !. J4.. - r v

\O) ( r- r..fi)( r + r..fi) + ( ...fo + r..fi) r

-c:: r_ -Jl--+ r + Y /Y -r 1 J\ = II+ Y fY

f = "\ ·- rx

r' A) (YX- r)(fXr + 9'X + 0.)::: f\ )L- r V

\r) (k- o)(kr + Ho)(kr + ok + ro) ,-··._...$~'..)'-"_. -r

~ .. ' :=( k --'ro) (I<. r;_tro):: I~ -l~'frc)

\A) fY X Of

= ( JL-I)(Jt+l)

A) -YX0 + HXf- \AXr

,.... r "'- (x (x·-Y.x--rtJ)

(" ,., ;- rx ( x-r)

\•) 'fXr + \'fX- \A r· r·

\\)y'-~'f :::(f-A){;jr-A)

r :: ( 'J -I') ( Q .,. r d r £) 1(

;.(rJL-1J(f~+r/=r(r?L-C)) (JL-t/) (tJ+rJ (()r_';Jt-LJ

. L r = - (X.- ,._. ~ -t r)

-- ( J(~- I)( JL~r) , - ( ~- 1 )tx-rl) (xy-r J

\ ~) X r + xy - ~Y r

r r'

/, ::o !C+ (;;Jxx-Y(}

~, ( Jt- r'J)(x-t-rJ())

\'f) xrn- yrm (m, n E N)

11 r . m r ::{J.J-(y/

:= ( )(. ~ ,., ) ( Jt ».,. ;i)

~)'far+ 'fa+'= ( (().-t-1}

H)l"'ar + Cla + r II-= t'(l.'+ .Ja.-rr -- ----- I;- -

r" /1- := f\ e.''.-.-~ ~I"<'<+ Y .4 = (f"CI-f f) (0-1} Jj t>,A:o(l'e>...f-f){i(;(-t-f')/""' - --

. ..t;S 1.5" J.f. IJ .r.j ..sl:..:.\;..;1 ._;..-J.:. 'f

'-:"' l a~"- b~" = (a- bY+ rab(a- b)

'-:"lx-y

v' I"

( ~c/: !L '.,_ /:J ~ ( X-t ~)- r 1t 'J ·'

- or_ r' 1- r' = r a -L. ~ n ' t- I j ~ ~ ~.

'}( -- tJ = ( ')'- ~ 7 -1 "~ ; .~ ;( . t';

~ : /};; -I- y [:/ _ vMl'F; /

a'- a= b'- b :~~[; a+b = '.fi r-I ' !

',l Y' ,./ '11 0

_,

l,.? J ,,~ I -"' llr. -"""

•. .?t- ~ ... ) '11-.1' ,_, I :, ·-'

. ..L.:.~ )} J. o)rJ' ISJL.; L; ~~ )} 15-""'l:... ._s\...>. 0 )~ Jl>- ._s\...>.~ )~ v ,,

' ·:J~ r r l " .. ' 1 ' c.-:JI ) (rx- Y.. r = ···- YAX + ... ":"") ( ... + oab')( ... + \Clarbr + ... ) = ... + ...

' ( '" . ' ( "" (

.~ .r JotS' ~/ J..:>L:.. ...:_, )~ L; ~~ _;~; '-:-"t.. ...:_, )~ Jt>- .s~ )~ A '~(

\

c.-:JI ) y'- ... +rr- '-') ~x' + r-x + ...

·~ ....,... JJ. \) _r.._) .SJL.; ~ )~ '..5""-l:.:> ~ 6:. ~ ~

'* ,, . 1/ J! ......

- a ""~"

(x + y)Y - fxy - (x - y)" -

rx-...{ry+' /-..:.JI)

x-y

rx-o ._:.JI)--

X-1

-._.o,l1)1

\ ,(-~·

I'

.__,) -T ~?(~

"

xr-1' ._:.JI)--··

xr-l'x

' "" "

d . ./ / y

..:JI.,e' *' J-J'J'.' _;;,_.T JS' oJI~I wl_,e>1 4A!.w ..;J,J'., _;j,_.T OJI~I

/

f

~,L_~->4-'N

L.~Jlf<''-4-.A-:­

lo .r> cr- '"; , .

( \.>, < • -~ .j.,__~ IJ 4~ ...>4-' JW:.

~ .. ·;· ~; 4~ WJw- .r..j .slt'"Jw- j16: rl£

·"',..,. .; ~ •''., .....

- r

TX+1 ~~_,..:;-1.5' J'..j _r.~\.i. .sl)~ X-1' ...>4~ 0JW:. ,x jlc>.r..~\.i. "'.::- .sljl "-:

a~"+arb .__,) · arb+abr

::

& •

'/

b

- l

I )(J{i _,

_C{ (a-d)(a+J) .0(6\.t-l) _a -=- . ..,..--- 1 - -

( ct - L) ( d+ il) a r( a - J) VL

r'a;1; fj(, --=----r- -r r r I' r""o Jl(/ r' .aX ;j

I

y+' yr+v ( <Jt-l)(reJ-rr;J ,)-----"" --

ry-r- 'fyr -o. ( r;;-r r'_X r2:1-1) ( ro -rj( ra -rr;J

r ,# r -j +AZ) -r I -()- v

( r cJ + t'J ( r?J-r-

It;) -l =

( )(

Yr r r -(-J-t~') r -"d-r'+2: --:J+r 11-r :::: - -==:.-_) /l- +-- - -(j- ) "<t-L =

t'(j- [_ cJ-1 t-1 " (a -r; c -::.

_, ~

y ( ~ -T') r U-r) '~"L?J-t) y

r ~-=-....1 J~ y ...,x ...::_._.,_; ,~~ ~ .r.'.r.x + ry «:ox- y ~ .fi A

= f -=':> \._C>'Y'...- \a ~ y fY\- -r L 't:') =) 1 t' J1- ::: V'"(f =1? ~ """____::_ d J T"

c ._:..lil- = A

B

c X = -- -) r'

X -1

'-cc'>A+C=B ~ c ;;;;:- .8-/1 =:- J(-f/ ( ?C--t-J) r

------= { X-1) (!X.-t-/) J.\(?'---l)(MI) ){ (J(-1)

- , J<.+ I ( X-1) (X.+!)

c - f]-;- .ll => - ){ 7( (:x-1)

._:..lil (-ox+ rxr + v) ...;- (x _ r)

-~--- -------

~+V

-::1-f-(

t~t..t/& CD

) ~-r

c> (y f + Y y + ') + (y y - Y + ')

7'-r ,.,., JL -rl' /- x -1- r . -'Xr-f;x. X..- {~n-rf)

( -)1'1-r) x-rr

(m -rtht-+-r (l'tr J

- <:.\...;_,().- t'

r + £t (j\. 1- ; --­_ro....

?~{~' ~ r' 1/

·-~ -+d -;r

/+I -:/t -;/-()

r X --

:K(-,t.-1)(~ I)

-- J{:r a

r ~;t-X

t::..-./

~!;i/c/-f"=/ ~(r~~-oc/." ~ @-} ~ <> --;~1) ·--­-~-~-Gl

~ J(-f

fX- I c:-. '= ~ -=> ~e.'

J ()... - : -== " =) o-_- \ ~ o =-> <J~-.. -::: I

' J ?;: ~

._,) v-xr = '/... (", = ~ · a xr tft-;;; ;;:- ~R

r ;-;- ~J; (liJi) /Jr 0 _ cJ =- "f ---

~>:.; - % rr -~ -tJ.,h -n - ~"r

r r lr"-rc) r(~+b} )X t(rx-ra Y;;t-;;'j U>.]l) -- = .,_ - ._,) )X i

,fr-o F-~ re+o - r x+-JY rj;-J? t'- t;) <Lx--o

r( /2-tt::J} -::::. -rc: -~ :=

-r a-1 !; -1 ( tt.--1)(;; _, ) -IT ~ ~/i-r/;l )--'I = :z(;-) ~) -IT :::::

( Va+1 ;; r r+r...ro (-~.;r_ rk (7\.-) at/\

1 \ )\_-M 1'---,;;z: - /'{_ -V: -::::. 1--- -JA.-+-M -

It )'_- ;:c; r' r, X-;JK-r'

/ I

_[ __ ='~:;I Jl- L £

r ' ( ;;_ f/) -t-{ liL -1) x r r .(; -f/ +'}{- r _J;Z -1- I rx +f -------------------- --~

( /; rl j( !;_- 1) X -J )(- J

._:.JI ) ---------

J<.. - '

,. 1j-;;:_vr = {/; J r:_ (;;: )~

(lr+lt)-r! ( ,/; +H Jrl l ' ==- ------ x -== ---r--r

~ ..fr+{r--' ( Jf-r/t;) -1 < .rr--rk J rl r ffr/FJ- J ==- ------

r/irk )rl rt/f- [ '1- = ----- - --

Y/i-L Y£ -I Y 1

r/\1

,)l__.ei-*' ...;nt. ~._;";yo T ._y 0)1~1 wi_Jfi i ~ ._;)H ~ ._;";yoT o)l~l

Jl:..l:.. ._sl..> ~ ,..L,;, r-' J J5:._;, "-: ~ y 4·~ r-' J IJ ,:.,T ._s~L.i.;) jl ~ ,~ r-' J IJ Y r!-P J_,.b ~')l.2JI ._s_,L.::.. ~ r ./ .

~ .::J_c "~_,(P J'J..> ·~J.JT ...:.......~ "-: IJ Y• o _, r. o ._s!... "':.Jij

~"tan r. o -tan'" r· 0

c) \-l"tanr 9-· 0

L::: v

<)-~ -·-=> 1[.

c

()

- --:= . ..o

-I'

X

. ..LS' & -f _/> _r- ": .sl .ili..<.; J~ IJ \... _/> _r- JJ>'-" J ~jl...: f• o '-:Jij \...X JJ>'-" ~ ~ L ,S -'::---:Y. IJ ~ •. bl..o \ •

r>1 :;: -t~n rJ. '- 17' -­r'

(}-'0" = ~v~( .... - ""·)

~ + \ =- ;-; ( y..._ -<>) "'-) d:; .;r 1\. - f' I I

=

/ • 0 • 0

.....:.Jil sm w < sm V'f '!--~)cos Q,.

0

- '

o< cos e < ' (._, o< sin 8 < \ (.__:.JI

r < I' 'R. - r-+ r ( , + r -=-> X <. t'v-. <. ~ ~ 1. (.·"!>\ \ I <'

sinx + 1+cosx r .....:.JI) . =-.-

I+COSX smx smx

Y(I-C_.,;r&) .-r .>,;, ':() r --- = f 6t11 (j

'< ( t-5,;/e)

tanr e ~ nan r e ('!"'

._,) ('- cosr e)('+-'-)= sinr e + tanr e · cos•e

frM>fJ-:: .f/,"g ... 1- CD..s'B=.>,n& :j~t? CaJ (J

"< ~.J, "' ft,/g ( t+ -1- )= s/,/'e + f/n '6> .,_ -'-

CoJQ OJQ

' \\ '\

r. , ro ,. , .f /Y) ~ r. .L. r

:= "'"' Q + -- =: J't;.., ~+ ~Ptt (1

\ --('1' tan' e

~'0

-- (\ tan' e

lr

r v"'c;r; + r

:= -~-----------= ------r = r + q., r-.. - I-t-a-v/1<- r If -I - (IF J

~ •'I

~~ B 0 C

I•

\A

I~ =----

r/r-r

.J.:.:l::-:IJABC ...:.J.';....::...,...L..,AD = f JBC =I· _~.jj5:..;.;~ ,._

5 - l..~ci.\-t.-:= \ 1...\o"i--X=-\-~~c r r "

=->

-a -d"' ='VV'.. l'V'-- '~'-o ')

'i - \ = E. ( y..__ " )

' -o-:=-E...1f<--+\

1

. ,/

~If -"\~ f-"

f11.A ll -:=. -= _,-" J.\.A- '}'._i1

M)JC..=' 'M~c.=

..:,l_.e.i ~ ..;;~)!, ~ ..;;,.-T Jf o;1~1 ul_.e.i i ~ ,_;;~Y., ~ ..;J,.-T o;1~1

:.Glc~u-IJ-...~~ C = [~] J B = [~] J A= [~J )"1

. .J.:S (""""J I) ABC .:..J;.. (U>.)I

\"' -='---::::-' -""'

-~- r ~v

-\-"'

. ..~.;-:L,: IJ A c.> ...h.<; .._,;, /' -~~ Cl ;.I;. l..L. t; ...h.<; ..:r..l c.> ~\.9 )"1 .~ )~ )) ~~ .~~ r J~ LJ J~ f J_,k "-!A c.> ...h.<; f

QfJ..:: D =:> /0- (_/...- (<>-o { = a ~ o,., [:] /};:: UJ <l <_o

=:!> ~ o 0 L- + 0~ =(t> -::::'!) (J '=(\-=!> -a-: t f,..,.) -tJ := _f[ld?~~ ~ ft= Jw1

=-> L- r r

=~--'-)' =~ =-:> _z::,o-.-;-\.,=1~-~0...=-1/\=:>0..-:::~ \" - ()._-+' - o-.-t L I 0

jl 6.;. i1£ J) ·..l.:.JJT ..:.......) ~ 1J 6.:_ .r i..w )./' .r- 3 ~ ~ 3 ..~.::--:~ y = ax+ b.;:_,)~ I...L:.:II; _r._j .;:_,':/)t,._. .v .1.>- v

011) Yy- I"X- \ =o

'\~-::o\'""--\\

~ =- r_'l'\.. +1-r r

""'-=-" ;JcA-:::l. r' r

~!'!! ._;-'./'

--.:.JI)-YX + y =I"

--------+---------·->

~ ,__, -----+-- -·---- ----

..s ... bl,.... ~ ..6:- ..SJJ ~ J_,h:

w'/!/J>/ J); /1 ~ \ A-= [~ J f/;'c;~/ _(if"/,., a ,, ~ 11 ~ c; 1

• !. ~--'()-=-dt/y/ftd?.C '• !-:"> o-()~"\-:::")C,-=-\

~ ..v~ if ._r..,.ls' .:>T .1~..<; ./' .r- ,.1~ J_,b J-.:1)11.: L.. .1.>-

'-:-'>x + ry = -'f

'd -z- L ~- '< '

"" ., - '- .) J :::r 'f

·~ I :~' j?~<P

)l x + ry = -'f

[_)-y =X

""-~-~ d-=" J

1 / ,Nflp~((J ......

A

\•

C-f7 ' 01~

[:']

c _,-= \' \ ""'-+'()

-a:::Y~-tL

':\ - "" u:::: -x-f>l-/

.'M--:::=. 'd~-d/f"' ~- I

~ --v...A -\'-L

/

\.. r~x :o~ C) "-

~. ·. (\ _., = ~ ('I'-<>)

'

r -M

- = r => '\~-' -=- ""-=> ""'""""' J11-l m- I

\V

0-1 d =----o:c -,-

" '( -"

d~

I \ \ '

d,:y=rx-\

0 -\:::.-L~,.,.._-L)

' '--() :::. - ~ "' ·-t- r"

t"'

-

d1 : - fX + ry + r =o

-tt. Y\1\':::.-=l'

r

d,.:x =a

d,: -y = rx

_'-"'/~ h.J.!/ /.-

. ..(..;.~ cSjl_,.. x + ry = -f ..k>. ~ J ~ J~ A = [~] cS ...kA; jl 6" ..l:-:~ 1) ,)o>- cS .... ~,~.,... '"'

"tl ""-~Jt.- r' ~ M ~ - ':.._ -1> _I r I' • I J.7-.-.3 r

J/..9-' .-

. ..(..;.~ cS).r r y J JJI L:_J jl-.:' ~ J ~ )£ ..s- rx + ry = f ..k>. cSJJ-r J _,1. "c c51 ...kA; jl 6" ..l:-:i-' 1) ,)o>- cS .._bt... r'

"- -=-1 => t' ~ l- n -t \' "i-=- L -'"'> ~~ = L -t- Y =)) '<\ = ~ -":? t~P <1 -= -v-... =") '1\h -;::. \

~ - c. =- \ c... 'lJ.... ~ \') -)> --i-:-~

.J//V~ c ~ fl ~./1 ~ ~.)'""' .~ ~IJ.::.ol 6.:_ )~ C = [;] J B = [:J J A = [~] .1LO.;, a jl...\1.. rl..tS' c51jl "c rr - '1 ("

¥"'--=.~-::. , ,.."'(\-l=f'(-r---o)=) ~-=-~v-.+r

c.~c~/!/ /JV<-->" ~ 13 =-c~J ~ J19

(A-::= \"'Q,\. +I-::=) -(QJ..._ = '(-==» ·o---=--9

-------~--, +-~---------~

I )A._- r ,.,

\ \I \

. ...:....-1 ~..o.x J.J><-A ..1. ~.r->- J ~)£ .s rx + y = 6 ..k.>.. ..SJJ r __;:. /' ""'._si...kA; jl-5" ..~.:--:~ 1) ~ ..s .J~t.... Y6

d ::1"~ \'~-t\"'= D ~ f"'1o..= (=-)X=_!_

o=~'"'-fl =>m= r=> r>'I'::-L ..)....! -:-! ,...

.=!'>m =--'-- 1- ,.... /lr3 r'

/">1- r'

{-ox+ ry = _,

.._;JIJ 'fy = rx + o

- f"~~ - !) )'... T \ <)- = -\

c)j...l -- l'l"-. --1- l.~-=- C:>

-'(-J..{ -D.,C+\'& :::--\ =-~'l

1-l''K--t ~ = cJ

\/).<._ = v -;>"""" \

I"

\l, '. d - o =:. I \¥. - , )

'-CI -:::. '\1...- 1

! m -+n=r y

'-::"') 1"

~n- rm = '· I

_\',..{ vt + ~ = 1' i" 4~ ~fr> =-q c==)

(?.. ~ 1'\-X"""=\9 V)1_Uvn::..\" -----j-----1--

. I 'I \

--:.Jil t- rb = _-r =--"J> o--._= \"o-f' o; Clb + ra - r -> ~ b f' ( rh i) / y- ..,.. )< - =(

(tt-'100.lf' ~ (IJ

> ~b-tYh-1\-=r

I I 'b = \\ =) ::_.0

:_,~J.:&ry-rx=' _,ox+ry=r.1_,b:-._}'j,;;~ji.S..~.:-:_,.:.:IJ~.J~t..... n

(~?-.,..ra=r

=> ~""'o -r"">'--:::.1

f I t

-·- ----+--'1:;-i ~--~---- ~ ~

! fj"'\

1 VI-'-.=--

[.

~ />. d ~.J /V_t ~};;,; d-" u~./!0.:/!( - ~ -

;J

\ . ..,l.!,\., ~ ......... y = -X .6:. ., (~ . ~ r J.

\ I

""'""""" ~ -=::> ""=- -1 .y....J-

u_?d¥L~=''

f'o-..~L.Ao :=.\Y ~ .1\'o-tL-h=!Y / v

cuJ~C!'-' rll =) b-=.)

' \ 1\ ,

c

..::.......~~I) t) h J.~\A.. ..UL y =X+ \ ) ry- X- y =o .6:- J" ~JY .1. ~ A = [Yt t+-h't~ i] ..s ...h.<; .fi iO

/,' <?- ~I , ~~·J-j {_J.J(~c.-J:~(yJJc}fs7/';' ~J,._py.) ->//_(~ ~

·..l:..;JT

"'Y'-'"':::..n

~ '"3 =- a -\ \ -=-> d =- \

( r i!-t h-e~ o

f- rvh = 1 ~ f= I h.+~ ttl

f \ (\ '

._j.)i) -rx + v = x - '

..;_,IJ6' ~ ._;;,;;' ._;j,..T .f o;l.:.l

wiJ6', .w.... ...;;,;;, ...;.J,.. T 0)1.:.1

'1''(1-'='1-C:::'tJ

'1--'a -T c (} = Y-t \ v

O....i>-::.V'""')~=C\

t+r -rt ~)-=-

~.

v 0

~ ( -t -t'<) ·-== V-1-.l-'<t)

o-\.-t\o-= -\L-\:

'----__~.~ ~-:=':.. \0 -=)

·- \ • ..,._ - I \' ""'- --\ \ 1'- -t e '-1 = o -=> - f ~ '11'-..= ~ L =J:> ~ -==-~ = - \' v J' t' \ f'f

,)r(x + 1) + r(x- 1) =o-x ·----

·"':JJT -.::..,...,..t: d ... ..s.r.;- Jwi L (. ... :-') •. bi,... j\IJ (._j.)i) ,bi,... Y

~ ( ~} ~> (~I}

A"' -t\ = o 1"-t L '- ' . !.. ~ r _., 4"1 '-'')A.~ &::Yr:

~ /'.-v...+\ -t'Y'-::::..0"'-Tl-t""-

·..\:JJT -.::.....-..t: IJ .r..j •.bi,... '-:"'1?."" -.s. ~ ..L.:.L V J Y .:.r.:: ~ ..s~...l>:- X _/1 r

X~ - "-X = o 1--~~I) = ( r; L _., .0 J '1 j

'I\_ ~ <J~.."- C\, "\-==-" --:;, ?C-. \. '\'\.- ~ )( ~ -tc:') :::.D =9 ):~~"=/) ·=-) ?'--== f"'

L .... -t ~= .=:) .,._:.-!"'

" L "' A • ..~.;-:l,:,IJ~~~<JT,.L;,L._,.M.r.l.r.JI_,:..~;~~~ol~c'-c"' kJ "-"~- _) ~+ J 'J(.-r '/ '}..-f./1

")A..~ ')'...-f' ,- -r "'--;-\__ --T "'i'---t'i -t-1A-i-J\ =/\ tJ =":> ~ -y..._-::;_ 1\ tJ- (, ·-? 1<. :\'

\\ J \C' 1 \DJ \'V', 1q . ..~.;-:1,:, 1,; ~~ 0 T •"": T ._,. ..::.....,...L: e>T .r.l.r........, r.S' L- J~ L IJ ->~~ ~,; .fi (C

='d

__;.li)Xr +OX- If =o

y '>'-- =- t::. 1'-t I L

....... -1 . ' ~ ~I I r~~ .

'U' -::c-P'l'-\'\L '1\\-j-~ () r.

__;.ll) Xr +AX -'fA =o

, "" r ( 'A.--:-~.._;_.e; ) = ( ~ ) == \ ~

~-\1\ry.., = + L /1

~-+ J\1\\..-T I ~ :::. -t f /1 + 1 Y

r ( 1<-T-f...) :== lf [_

• 0

'<" -1

. .J.? ~\b. J C>yjT .fJJ jiiJ ,r,j ..:..'ht..... o

";-") YXr- X- \ =o

c/ /. / ") ,/ r /,.- / ,.-J~

~/ ~e;;: tJ/..J~ .X./ ~..J/ J'!rr·

r I / ;~ "r "L ;.._c /.,;~.(-:-;::'~ 'J-/~_~;U: q.t7..-v.v

•.J../1//~/

. .J.? ~._,.....G»._;JJjiiJ..r.jw'i~t..... 7-

__,) YXr -X + \ =o

I

,/' /

_;1;/PJ/~~).~- -'·r;-/.:ri;,.,,~~:

' y..,'\- ~ ....... ""' L =" =)Y...I-; ~')'...-l.

" t' r '

' v \ '

. ...l:_ T 1..5" ..:...-...l:. _r.j J _,..; jl .... bL... ..:r..l ..s~l_r:- .J.? ~t; '...l:~ __.6 J~ IJ ax r + bx + c = o i J~ ~ J~ ..s ... bL... A

~ = b r - fac .s- x =

c_)Ah 1- Hh =-\A

A k"-1\h -\-\1\=o

0'-. =A 1 \, -:...-I r ' c_ = \ 1\

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