{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Answers by the good doctor
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "factor(4*x^2+12*x*y-20*
x*z+9*y^2-30*y*z+25*z^2);" }{TEXT -1 24 "The trick is all the *'s" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),(%\"xG\"\"#%\"yG\"\"$%\"zG!\"&F'\"
\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=x->x^3-9*x^2+23*
x-15;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operator
G%&arrowGF(,**$)9$\"\"$\"\"\"\"\"\"*$)F/\"\"#F1!\"*F/\"#B!#:F2F(F(F(" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f1:=unapply(diff(f(x),x),
x);" }{TEXT -1 12 " Or f1:=D(f)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
f1GR6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"#\"\"\"\"\"$F/!#=\"#B
\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f2:=D(f1);
" }{TEXT -1 32 "Or f2:=unapply(diff(f1(x),x),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#f2GR6#%\"xG6\"6$%)operatorG%&arrowGF(,&9$\"\"'!#=\"
\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "solve(f(x)=0)
;solve(f1(x)=0);solve(f2(x)=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"
\"&\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&\"\"$\"\"\"*$-%%sq
rtG6#F$\"\"\"#\"\"#F$,&F$F%F&#!\"#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(\{f(x),f1(x
),f2(x)\},x=0..6);" }}{PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6$7S7$\"
\"!$!#:F(7$$\"1+++]#HyI\"!#;$!1o2CN$pV@\"!#97$$\"1++]([kdW#F.$!1o*4lWq
%)*)*F*7$$\"1+++v;\\DPF.$!15Ti9zzGwF*7$$\"1+++D<q8]F.$!1uxMLS![g&F*7$$
\"1++]P\"*y&H'F.$!1[u%Q^lu$QF*7$$\"1++](G[W[(F.$!1eXQ2)R!3CF*7$$\"1++]
()fB:()F.$!1*>.%z*o*G6F*7$$\"1++](Q=\"))**F.$!1feHS?w8&*!#=7$$\"1++vj=
pD6F*$\"1$f+Fy*HF\"*F.7$$\"1+++lN?c7F*$\"1H'G+>/En\"F*7$$\"1++]U$e6P\"
F*$\"1Ob#4(e%Q>#F*7$$\"1+++&>q0]\"F*$\"1k[QtlcEEF*7$$\"1+++DM^I;F*$\"1
Y`')eJ[4HF*7$$\"1+++0ytb<F*$\"1El\"3Z'p]IF*7$$\"1++vQNXp=F*$\"1')\\S.X
>xIF*7$$\"1+++XDn/?F*$\"1LQ)*e?E&*HF*7$$\"1+++!y?#>@F*$\"1;wl#*H$)RGF*
7$$\"1++v3wY_AF*$\"1)*>Lp\\SsDF*7$$\"1+++IOTqBF*$\"1*3_fm!zoAF*7$$\"1+
+v3\">)*\\#F*$\"13TZZyev=F*7$$\"1++DEP/BEF*$\"1\">UT5hUX\"F*7$$\"1++](
o:;v#F*$\"1LL*yPK@y*F.7$$\"1++v$)[opGF*$\"1;_[)\\u/>&F.7$$\"1++]i%Qq*H
F*$\"15S_-Ch%=\"!#<7$$\"1++vQIKHJF*$!1Lw<&)HH^^F.7$$\"1++D^rZWKF*$!1d.
/7V'Hj*F.7$$\"1++]Zn%)oLF*$!1y^/ch?D9F*7$$\"1+++5FL(\\$F*$!1YB#[l?j'=F
*7$$\"1++]d6.BOF*$!13wz\")RG]AF*7$$\"1++vo3lWPF*$!1;'Gt!4plDF*7$$\"1++
]A))ozQF*$!1[J'>'f+QGF*7$$\"1+++Ik-,SF*$!1gHCoK-,IF*7$$\"1+++D-eITF*$!
1-ih!4+s2$F*7$$\"1++v=_(zC%F*$!1(z)Qr;D[IF*7$$\"1+++b*=jP%F*$!19/z=$y
\")*GF*7$$\"1++v3/3(\\%F*$!1U`wU0*Hj#F*7$$\"1++vB4JBYF*$!1DjY<[f:AF*7$
$\"1+++DVsYZF*$!1AaYm7cd;F*7$$\"1++v=n#f([F*$!1*RZf\"=J@!*F.7$$\"1+++!
)RO+]F*$\"1dm(o$\\j7HFU7$$\"1++]_!>w7&F*$\"1scqQ1v?6F*7$$\"1++v)Q?QD&F
*$\"1(\\\\O<kMV#F*7$$\"1+++5jyp`F*$\"1/TdesIHQF*7$$\"1++]Ujp-bF*$\"1n'
\\%)fD[m&F*7$$\"1+++gEd@cF*$\"1&3@c!H%3`(F*7$$\"1++v3'>$[dF*$\"1\"Q<%z
f\\l(*F*7$$\"1++D6EjpeF*$\"1A'*QG&H_@\"F17$$\"\"'F($\"#:F(-%'COLOURG6&
%$RGBG$\"#5!\"\"F(F(-F$6$7S7$F($FUF(7$F,$!1+++X-`@<F17$F3$!1++vITD`;F1
7$F8$!1++]*\\qkd\"F17$F=$!1++]'*y<*\\\"F17$FB$!1++v^EDA9F17$FG$!1++v-J
$4N\"F17$FL$!1++vSe3x7F17$FQ$!1++v'*Gr+7F17$FW$!1++v\")[eC6F17$Ffn$!1+
++hyFY5F17$F[o$!1+++X*\\Ix*F*7$F`o$!1******H)yl**)F*7$Feo$!1,++]%>p@)F
*7$Fjo$!1******pJdluF*7$F_p$!1,+]n(yKy'F*7$Fdp$!1+++IZ'>(fF*7$Fip$!1++
+?`n%G&F*7$F^q$!1++]ZV>&[%F*7$Fcq$!1,++?#=vx$F*7$Fhq$!1)***\\Z`3,IF*7$
F]r$!1)***\\UwthAF*7$Fbr$!1(****\\(eI!\\\"F*7$Fgr$!1(****\\(p!*=yF.7$F
\\s$!16-++D#px\"F`s7$Fbs$\"1(****\\K#QfxF.7$Fgs$\"1,+]2H'oY\"F*7$F\\t$
\"1*****\\[!38AF*7$Fat$\"1)*****fi*R)HF*7$Fft$\"1*****\\%p=QPF*7$F[u$
\"1++]7_!zY%F*7$F`u$\"1*****\\$H8y_F*7$Feu$\"1(*****z&eh+'F*7$Fju$\"1-
++]8[$y'F*7$F_v$\"1)***\\78&y[(F*7$Fdv$\"1-++IP\"zD)F*7$Fiv$\"1)***\\_
C[#)*)F*7$F^w$\"1****\\Ub')R(*F*7$Fcw$\"1+++&fM![5F17$Fhw$\"1++DJgbD6F
17$F]x$\"1+++)Q=-?\"F17$Fbx$\"1++]J9dw7F17$Fgx$\"1++DLAH_8F17$F\\y$\"1
+++'yr=U\"F17$Fay$\"1++]0yh,:F17$Ffy$\"1+++'fVHd\"F17$F[z$\"1++Dl<**[;
F17$F`z$\"1++vm&z<s\"F17$Fez$\"#=F(-Fjz6&F\\[lF(F][lF(-F$6$7S7$F($\"#B
F(7$F,$\"1n9/()>sp?F17$F3$\"1[\\.%o2x(=F17$F8$\"1$[hJO\\5n\"F17$F=$\"1
/=Y/`%HZ\"F17$FB$\"1*eTy$)ocG\"F17$FG$\"1&yan?]37\"F17$FL$\"1aW.s`B\"f
*F*7$FQ$\"1m9=q@E9!)F*7$FW$\"1Z)Q)oH4RlF*7$Ffn$\"1Fh:?!yC7&F*7$F[o$\"1
V?iNaPfRF*7$F`o$\"1:qO?#p[u#F*7$Feo$\"1#p:tV![E;F*7$Fjo$\"18l=(H_cW'F.
7$F_p$!1cIlo4%fl\"F.7$Fdp$!1m'p>xpz-\"F*7$Fip$!1s&[o*Qos;F*7$F^q$!1oh4
sfeBBF*7$Fcq$!1r183I'3\"GF*7$Fhq$!1n]3GsX\\KF*7$F]r$!1X:/.>rtNF*7$Fbr$
!10<\"**p:\\\"QF*7$Fgr$!1[-V6R0\\RF*7$F\\s$!16p)yot***RF*7$Fbs$!1/a%\\
lE)\\RF*7$Fgs$!1`+bnFp?QF*7$F\\t$!18gdIi&=f$F*7$Fat$!1l@pE0)zD$F*7$Fft
$!1OENIl\\NGF*7$F[u$!18'45D&[OBF*7$F`u$!1$o0nsU%y;F*7$Feu$!1JOC$f#QQ**
F.7$Fju$!1$[o^k]Ol\"F.7$F_v$\"1oLU)RkKs'F.7$Fdv$\"1ton(fhFo\"F*7$Fiv$
\"1(>*y]#\\Ps#F*7$F^w$\"1Y#)\\l]T0RF*7$Fcw$\"1,,k-w8`^F*7$Fhw$\"1F/OiJ
IdlF*7$F]x$\"1=VWd\"oV+)F*7$Fbx$\"1')Ho(\\)G!e*F*7$Fgx$\"1gNU.>\"R7\"F
17$F\\y$\"1E!>l9mZG\"F17$Fay$\"1k)G[pY!z9F17$Ffy$\"1Uy\\jHzh;F17$F[z$
\"1F>b,#yf'=F17$F`z$\"1\\[1(RP/2#F17$FezF[el-Fjz6&F\\[lF][lF][lF(-%+AX
ESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(Fez%(DEFAULTG" 2 425 425 425 2 0 1 
0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "evalf( exp(1),100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"_qFk
;D&y@QrXfZNNIm2Cxinp'\\df**p$4Zsv(\\iENruGg`BX!f%G=G=F!#**" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "solve(\{x+y+z=3,x+y-z=1,x-y-z=-1\})
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"xG\"\"\"/%\"yGF&/%\"zGF&" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(\{x+y+z=3,x+y-z=1,x+
y=2\});" }{TEXT -1 53 "This one has infinity many solutions, one for e
ach y." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"zG\"\"\"/%\"xG,&%\"yG!
\"\"\"\"#F&/F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "solve(
\{x^2+y^2+z^2=4, (x-2)^2+y^2+z^2=4, x^2+(y-2)^2+z^2=4\} );" }{TEXT -1 
43 "Check out RootOf in help leads to allvalues" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<%/%\"xG\"\"\"/%\"zG-%'RootOfG6#,&*$)%#_ZG\"\"#\"\"\"F&
!\"#F&/%\"yGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "allvalues
(solve(\{x^2+y^2+z^2=4, (x-2)^2+y^2+z^2=4, x^2+(y-2)^2+z^2=4\} ));" }
{TEXT -1 35 "Need evalf to get numerical answers" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$<%/%\"xG\"\"\"/%\"zG*$-%%sqrtG6#\"\"#\"\"\"/%\"yGF&<%F$
/F(,$F)!\"\"F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "evalf( al
lvalues(solve(\{x^2+y^2+z^2=4, (x-2)^2+y^2+z^2=4, x^2+(y-2)^2+z^2=4\} \+
)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<%/%\"xG$\"\"\"\"\"!/%\"zG$\"+
iN@99!\"*/%\"yGF&<%F$F./F*$!+iN@99F-" }}}}{MARK "13" 0 }{VIEWOPTS 1 1 
0 1 1 1803 }