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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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