0% found this document useful (0 votes)
17 views12 pages

Math Enthusiasts' Puzzle

Uploaded by

victor.avargas07
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
0% found this document useful (0 votes)
17 views12 pages

Math Enthusiasts' Puzzle

Uploaded by

victor.avargas07
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 12

1-t§* o r E-taa- ,y

$ X'- I : {rit¡vrc:-,'} ao\"$e'r lx, : I


'/.-- -q
Y'= {
y, 1ñr
X"l = t!,
X,' 4,
Xt ,'2

A St 'J,s t (c,c o) 5J*.,*^ ' (,.


2_É'- lrbx -c ?6
55i
{r'- c
¿z --D,
5 =(
cz -gt .(E,i)' ,(E '+)'
("-f5\ t.(E)'=(#)'
Í''ft+g=!:-z* t,= vrlj
(t - #)' ,,# t, =
to to
3
/o

- I /É
'LI - ó1"5 =-7o
t,- , JÉ--D
tc tO
t= !é!):
)o to
t"> e

5 z y'^y =Aru,),,¡.) 5§*"**"1,=L


31, _y __ z
t+l'-{á +)' .?

. (:)' /,.
zvz
f-'t-2 t) .2-a .L
33'2 -%
Y' -¿r tel= *'a ú -)
/,'é t-L
,t)'
(y - _2e-- -r
_J¿
G

6
tll r -vl
ñjTY =: J-€
Y-t -:+ rl
/1'6
I
v - '-"á :2
¿

y=*r+ /n
4
r
(.a
ti
v' ' -7
/'z '2.
.J
>tr"- ü', l, = 2 LLrá" </o"qr,,
0 b y'- 2,o Y + lb 'o (ft'ol* ''¡'''¡'¡)' ;
I -orac -'ql
2(rl'-,cy + a)=o (c,c.^r;
t (tt)?- Io Y(") u) , c (r. r,¡¡,br ,.)
+
L,á
t
1 (tv - a )(ry - v ) = o (r,c.,{l
?
zLYt y-2 )ét -q
- q'--
/J
x =O
t(v- 2)Pv- ,) ,"
R(y.z)=* 2(w-q)..
2!-q = o 6/-g:c
LY.1 by= q
y. +
t/:r / =*a
,/tY: ¿j
S 6Xz=a/r-3(r.o.*J)
tX7-3/zt3.o \.3 >N,.*; :X, - L

3,{'*b:c b-o
C=7
N= -o:l@u§¡r' L=-i
n,r9t
-[.|- Í,=i
= !\6; e

C
lz=S¿
C

Í=LL¿
é )lr r-i
d ¿?'-!=o ¿r,"-..plJ ¡L*',Q, -§ Z

J.?, = L
¡r?-
v --:?| ?,,j
¡?2
4 Z
'lt : )*
?=!'f7
P=12
r",
?,=-E
,7 n=- /s
z
m2 +21 = ,n úá /o*s,
([.ü,.--",]\
4:l 5§*'*, '. Yn,
' t_ frW ü-loe,t/
yn¿ +{l'm = o li
t:-l
Z
2
rnz-w.i2l:c c'7t
If): 1l Y\z: I

Cr)z- v('I;r) a

2(,)
'!J!:il ,
^
- lt,lZ,
2
jr

h,. I + fr, , tt: \g!L


fr
4_ 2
yrtt \83L F-'
= /- + /
-L frJt.*- ,t6zc
¿
2

8) k *?,)t = q(u+3) G,§"*"ri


(il',zp¡¡¡z) r (z)? *X
= +t z
e.l 3§*d- .X,,1+{ G
b,-rl
Xr+rl Y+t4:bX+t?
C, -B lz,1-1 i?
x2 - qN -F --o
,l ! /,r.-;¡ i -?l
r( t)
=tl+'tl;rb,
¿
=,t Lr[W
,
* 9!1ts
2

l, = 'l +'l t,, Xr={-'/G


2 2
= 9'z-*9lz
z
= 4 --!l=
Z7
{,=2+2,12 tr'2-2€
', X,=-l +c 12"f". t/r^.1*
4) x' + 2 X +l "¿ fg,§,-.,.) )

Q'l
sMdü B- qac -"t1
Y, 'r ! /{,1'- {(r}r¡ b,2t)
a'- ¿
Ir.' -! - i
4
I Yt=-2t2i
- _t : \/ _ q
, t*-_
2
4
--at9¿^
--q

=-r:E- X,
LZ
--'l r¿
Z
-- -l !lc'
Ir'=-¿-2i
L
lr,-l-,
(sx - !)(2x + 3) = X +2(( - l) (r.q.^--l)
§*,"" ' X, +G
ru)
--L
=
i6
(a[r)x: *fe[s) * (-rXdr + (. r[c1 = X + AX -Z
(y2+Yl-3--sx-.L --L iá
Í,¿ 2- -
-!= c
='
6x2¿(/X JG
Q ,C
/ =-tl1ffiqeñ b.1
Cr-l

t?-

=-1!,lT;
____*TT-
,-qJ{m:
T,L

'-q !.? ñ'


rZ

{, ,-1 :!Ñ __4


Xr =' q 'Z (to'

"J,rr+
t.t
,#ry IL

,/ - -)Z o-@
At. é :-*--W
{z 3(
f0 tf -l)'= 4q ¡v'á'"*:"u*J q /:,á aJ,
S"[^t-;'.X,= 8-
?Aá-ty
( x)'-z(x)[z] +(z ¡ ?= tlq
l'-qltt{'qq )(2. -b
y'-'tY - L/5 -o (r' f?r b{,cJ
(r-q [r +s ) :o
f -q lo xts,a
{ -oY
tr,t- {r= -5
fz) O,{/ - o, Sy? =o (ine*.?1er¡} 5d."-*" I [, = ]., I
0,5['-ü,Y: = 7¡
C,5y'= O,12 ft = -1,2
vz- o,72
O'5
(..=),1-Y
tl- t or85
l----
e ll
Y _1 !,L

{,' 1,2 f,r-!,2


rt t,l¿z-L,tú +§,5 =6 [c t*-* t)
L,L t' 'L,z (. 7c¡ ! sQ
3 Jrdd^ ', t,x o, Y o
-n - TI--!,J

€r"0,¡B
{'- l,oll€ ta,)Y=o
{t - {,oq ,t +(ry,)' = -o,21 + (OJ]'
('- L,al ¿ + l4flrlf -o,eyr l, lg
L{ = -A-
k -ryf
.1

A r -----r- ', lq
---!,c:st!,t o, fJ
Ll

A,l )
4' q

A
(= ,,c1r
I o' 33?
2 4
l-

-€,=l,Oql+a,33t tt: t,agl-0,332.


7"2 Jz
= !,'!zz o.lsq
2 L
t,t-0,YO tt?O,b8
4 12 +z x =o ([,c,'-'] SÁrdd.i /.,4 -42"/
)(, = o 8-?CIa -cl
f({r3) =o
Yr'-z
t' =C

/ +g = o
V - -,7-
Az- J

O -t - X =€ tr.e"..*,,\l l-1,ii'.1ü I X,' 3*r/1.1


Á:-_x-g=c
36
*l*-6rx) - tG)," q
b--G
--.2.
Xt,3-{A
LN? -6x -5 ,e c. -5
)( ,llFrt'- jl:tlt{
2( 2.1

=e !¡V;;vT
q
-ut { 1T

Y
=n!z@
q

X, - e +2,1fr lr=-G * zfq


q
Y
=6+2ffi
Hta <G'Ztftq
--
--¿
qLl
-3,{tc
t¿> - {r,
--
z2 ->Z 2
l,'2= 3 *(t1 ¡r= e'fn
A0
ro) tr -r-YZ =o >n\",";'. [,:-9 nl''\*\*:i
Y2+(-tz =o tT'{z*Lrrc} b'\$^'i$
(r* v )(r*E) Y,L -- b
I*9=o V-3ra
(, = ''l
f"=3
r$ ur'-L{T fi+2 :6 q.l (r ol S*L*'; I u),, ,t-
- \fi
rJ:{fr t/fteQTi b,
C=
-1¡?
?
2G)
:/üJ vt,lQY s --1
t
=2iz!,1 ó-B t

q
.<.

,-z ít jo
2

Lü =2 {i
2
tJ=fr
',,i) y,-t=¿Yft.c''
+ 5}*"d* ', l, - !6,6
4 y'-Lv'é,"
-0,ll
1J

tos(} y,)- rcsllu4 ,,'[é)'o

E" -trl-E=o
y'-sv-!=oÚ5r+;'
Y' Y;/tff =
( V* 9\2 scY r t? oa9- tz scct
L/'- a-I - tec>---_- r8o

l- 9- =r ttl,6'lg
v- ttq *- !!t,5!,=iu'
/'c t9J7
(l J, Eq'r
/? -- Z -
Y,' ='17
, t * Iil,Eq'r -*651,58tclt,6q t/ 'lq
G t3tt4z
-1- E0, S¿ É;t?
: t32á,éqLl = C51,18-G'|!,aGq
80, gz
&,s?
= -:::!§j
l, = !G, tt bó,57

/z = -o, l\
q) 6X2 +7x 's;6 (e'c il
ür\*\*'sx
Q((+Jr-9'o
GCÚ =§".*
', {,. i B'qs"-*lt
l'rÍt.9 :e
GI l,=-2
"b
t,rá, r(l,i)" tr(: +)' X.=.1*b
'Ít?
l'r*r+ffi=9oh .C
t?
Ur#), =wr# '# X, -,

ffi
?

xrá=!fi
^[GGr=:
I =-+: ft
lo) x' -6x +,s :o tv.al
'L - >J*¿; ', X, s +21
=
¡= 6!¡¡fr,*¿¡.r
I

-7r--
'l: -é
Xz :
=
¿. it
3-2i
= t,l tc *V-_
e
2 l,:6+qi lrt4
= a! \t:te - 2 Z
q
'_9 - ¿(
Z =L+-L.
4¿-L z
--e t {c Z

/ x, : z +7i /, -- b-2t

g+L
2) x' '- Gx +,0 ' o§,1-, _ , 3\"c,ó*" '(, =
X=,61 .,@{,{T14 ,,-, e -i
---7A-- c = ri
xe=

=etrE{-qc
2
=.i_E_
'7-

'6!_4

Í,=a*2¿ ¿:6'ti
7- -2
;É+2.
LL
4L *-g I
- &' .

(, =e+i :3-L
I
$ax''qx+t=o q=B
S§*.*. '. X,,j t r i¿ §.§* \*:pn
g-\to-q1
t,,Lt /({qB[
__c,| I b. -q

¡-,
,9Jülb -b2
la
-.r:,f-te-
tb
- tt !,[t6 L

t6
-- 4 lol¿
IL
l, : Ll + ,l t Xz :J::!:_
t6 tt
L/:
-Ll
--t-L
té /6 té tt L

l,-Y"J¿
"t q L-l {. =L
"L q -
t
L.l
¿

,-l,
5§'"'l'"*" c G¿
X' =
^
-+ ..

x,-tlit
--7O- f:, Xr:_)
z E¿
.llJLL- ¡)
?

./.

---t1,/z'
2
-rtJá
. __-v-

/,.-!*€i Xr,-J_rE¿
Aa-
Y,=+-.Fi
zzzT lt,J ft¿
,,rl Y=t'+Lr-1,5L2 q=l ilt§* \*sA
- L T.FL
o = f 'rLx - j,su¿
b= L
c = -1,5 l^ --'-T- b-ttq"q1
Í =_L:@
/[,]
_ _11

_ l+
2
:-L!L{7
2
X,='L+L'11
?
X"'W
f, =-L+I{L y.,4U
/*

] "',Y. . -l
^t +{Y'L
0-,.r,-,.-.r']o
I tf
r$ s = ü¿t -! q,'i¿ : t\6Ys á : t,: ulos
st¿ =te6 *7g
,J; \

C--¡
J-L' g=e,b*/Sz l1 ,-)g =-9-L, t/", cJ,\.o \o,ü.(e ' ''lot¡
!j;( -it('=a f =! c= ó 1 90.^
\tiu*
arolnf,Ef llc)'-rr.
)t-l*,"
o\^

tt¿t-t*c ü¿ = rtc yg
2
zd¿ú - 3 t?.c
Ttz -¿ rJ; t '- o
(",r-tl;l/ffi

r1,5 /u-t
:392""/9!W

=:" Ytr'!r!rft
t?, a 2/rt t.

tt = 3?? 75+Sot Ys
t2= 3qr Ys- 312 /s iv
Sn)§-ñ^.(r=9ó¿
-Tjfr-W- @a/,
=*!_8,1__y5 =
t9,6 g/rz , q,275
€, = VOs ft = Og
24 4¡ 3 \'l h§* \'Yn
s-tto-q1
ü-r r 3
cJz q -3
Z
J)-+
L)q,^ -r

q) l? + bx +c :c q,= 3 0 *. : t".¡
5J*.** ; xt -Jy -r[ : o
(x-0,)(y_r^r)=a
(y - t)(t - ,t)'= o
LL, 1' r ¡' r''t) x r (-r[- u)]- o
(v'-lt-tz)=o
x'-'tr x-u. =e
0-' : ,r' -11 - tz
=o
b) {'+bx +c:o A, = 'l Qt,3 s"\"-; ', 1,"
'2 N -s 'a
U-a,)(x-or)= c
(y + t)(x - z)'= o
r(út.l,o
[_U)rn(-s+)x
(x'-zx-3),o
X'-z'x-3 'c
V,',X2.2N'3 =a ..

c) lz tbx +c ,o A,=4 A7:_-2, 5*L**¿',2x?-x-G=a


(t 'o,)(x -a,) 'o
' (x- 2)(x r 2)= p
[1r1' r ¡', + l) x + kY.1\= u
(x"-fx-3)=o'
4x'-it'sJ,o
zo
2)(z-Y-6
\r .: {,t'*y
:.'
-6 ,a
¡) rz+b v +c :¿ A
U t = -t7,
..
Q,
-t
,.r-i s*\-,*r*-: 8X2+dltl=A-
(i--0,)(l-ar)=o t"- ::

Qt tlu r+) ,c
({)' +(+ ,i)x +ft)(il =o
l'ri-X+á=o
-4 2 .

8(x'+ +r * 6) ,o
8X'+aX+l=o
0..i bxu+oY+t=o
r\
,rl P x ü-)"J P
A-l
=A-\**¡ r
t'§* I"^5"\
ü\, [. Yn r],É<rl¿
b'qb6 -ql
Qr=lrmop- lmop2
6=t2ooaf - Luof"
q: 1000
twF'-ttwof=c b,'l? ooc '.?, = tL
(= C
S§.*.; . ,

lo:tzooa!@' t2 \ü€-ñc\, l\ \*''" \.


y*l u'§v',.^tY*
--lzoac, /ffi \ o"\'-x' \s- "5*"1
o

-z(,
- t2 acc !
2 C,OA
l-z @a
\-!L¡'fD r

2 ooÓ

F, = t2 mo +/Z aac -
Pz = /? oca - /? óCa
.2 ND J@ó
= 29 Aee
=O
l,aa:g -/ uo
P, : t2 t'z = C
frs P, = Lt,

You might also like