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(!egA +.2Ch ڎe3eot#0+l>: OU&bܱR߱Wmǵ\KZ- ns޵,]Yxj,.e-%IUپhUl}^2۾}{BP̢ m*HP/hY\&iel.%*r'tL:@Ok=/҇C_XA=MBK,h@M8tWj܉ƃt?x?/y0 Tܦ*a}>6x3W|x}Sn@vL"$`wUJH,*, ȱlj3iw,I%˧p9^_я'-_Q&iJH ǹXK@tS'ơv&nT *u,Sʞ֐yue/_t%땞5/ܝR_> iztv8OP2X#Nq[Zy]GGxikIsΈ?I0l(Fha|Ea.RO{'K5q֩d"deN݈ܨ/& XVz32L'0dCjޔc|ʮL7 Q Rnc+?iXw"Ej .DNW&΂b^{`)`g#)1Q|UgdCGmC;-}0|& Tv2e{M (Ktx}So0~izhU!퀄`iN]2 iݍGn?vK{{Z؆;5rITl\q&e9~@c_ \u`?7`甉, 3j 4ZFðmJV1M؀G#a侔yRS7 @B2\Yz}4B0 fk͠{6i сdnxʝuW恟uG'uI;NI80l `BZ,EY\MV62'~B.ԉI;^L媱iTOE֎fU$ 6{#Officef/ Microsoft Office 98L4Macintosh HD:Applications:Micr(   F0d 0d 0d0d0d0d0d0d0d !0d!"0d"#0d+$0d/(0d1*0d3+0d6,0d8.d:1"MathType Equation Equation0"MathType Equationd;2"MathType Equation Equation0"MathType Equationd?3"MathType Equation Equation0"MathType EquationdA5"MathType Equation Equation0"MathType EquationdC7"MathType Equation Equation0"MathType EquationdE:"MathType Equation Equation0"MathType Equation/0(  0;[0 0 000$([\{b00 000000000  0=] 0 0 0000 2 3 !A0C0E0G0I0c00000000000000000!%),.:;?]}acdeghijklmnopLDTimesg|g|g`y!gpy!xy@  @@``   @n?" dd@  @@``  tF   B$#]^sg^gyxB$<|ڟ~__yxB$ߊs MhvsHwxB$Y 'dsNer0 xB$Ƞff嶦ghxB$&Ɂ )k}wxB$ni7{-n_xB$ ߩ,-%Uezc? xB$ $5c xB$#U[rV}vsxB$5z7+~i H2A!xB$nJQ$YF%xB$M8re)xB$pz6!%%+y^,xB$͢꭯;rh q/xB$N"QF6Jtj:H3xB$zëI >޽\6xB$e|VaX:xB$M-dkn\w>xB$CK2i.&f<kAxB$p'eV|NYEExB$ܦ*a}>6xIxB$v2e{M Lx `1?0 i=@ g4kdkd!4ppp@ <4BdBdg|gyg? % 7.5 Solving Radical Equations&2001 by R. Villar All Rights Reserved'' Solving Radical Equations"(To solve a radical equation, isolate the radical. Then raise each side of the equation that will eliminate the radical& Example: Solve .y  Example: Solve, (The radical is isolated& so we must think about raising to an appropriate power that will eliminate the radical...rr%Example: Solve, (Isolate one of the radicals...0!The Geometric Mean of a and b is v"===1For instance, the geometric mean of 4 and 36 isH2%9UThe Distance Formula The distance d between the points (x1 , y1 ) and (x2 , y2 ) is Vi% Example: If the distance between ( 2, 12) and (x, 6) is , what is the value of x.Zd &0(<%P ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|? " dd@   " @ `"  n?" dd@   @@``PR    @ ` ` p>>! |(     `Ƨwawa1 ?P   T Click to edit Master title style! !@  ZƧwawa1 ?   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     SB  s *޽h ? a( &Microsoft Office 98 ZR@( P @  Ztݶwawa1 ? @   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     Sp  01 ?    B  s *޽h ? a( P 0( ?  B  s *޽h ? a(( 0TP(  Tr T S $ç` @0    T S ۶ `  <$  ! H T 0޽h ? a(A    ` \i (  \ \ 3 rݶwawa1 ?     \ 3 r4޶wawa1 ?0<$  ! "  \ <A  1?  8  $D   \ H1?` ,$D  OStart by isolating the variable B  \ H1?p ,$D  0  2  2( \ BA  ?1? 8  $D   \ H1?p` *,$D  tBNow, eliminate the radical by raising both sides to the 4th powerCC \ BA ?1? h 8 $D  \ BA ?1?Z 8 $D  \ H$1? 0 T  ,$D   [x = 1288iii  \ H1?@ : ,$D   a/Be sure to check this in the original equation.00H \ 0޽h ? a(, x   PhT (  h h 3 rwawa1 ?`    h 3 rwawa1 ?<$  ! " h BA ?1? 8 $D   h H41? ,$D  tDRaise to the  reciprocal power...## h BA ?1? 8 $D  h <1? ,$D  PSolve this quadratic equation.  h BA ?1? 8 $D   h BA ?1?7 8 $D   h HT1? p W ,$D   fx = 3,  18 iii  h H1?  ,$D   k9Be sure to check both solutions in the original equation.::"  h H1? F  ,$D   v$(x  3)(x + 1) = 06  h Ht1?4 ,$D  Z(  8  8 h <1?  ,$D   ESolve by factoring.H h 0޽h ? a(k    ` l (  l l 3 rwawa1 ?`    l 3 r4wawa1 ?<$  ! " l BA  ?1? <8  $ l BA !?1? 8 !$D  l <1? ,$D  R Raise each side to the 3rd power!! l BA "?1?j 8 "$D   l Ht1? T ,$D   Yx = 28iii   l H1?0 [* ,$D   ^,Check the solution in the original equation.--Z  l H41?p ,$D  R2x + 4 = 24  8x 10x = 20@*:  l H1? p| g,$D  2 2x + 4 = 8 (3  x)@ l BA +?1?[8 +$D H l 0޽h ? a(  L D p p (  p p 3 rTwawa1 ?``    p 3 rDwawa1 ?`<$  ! " p BA /?1?@ 8 /$D  p H1? d g ,$D  Zb = 548iii   p H1?p 0r ,$D   a%The geometric mean of 6 and 54 is 18. &%'  p H41?},$D  {7Example: The geometric mean of 6 and b is 18. Find b.(8 -  p BA 1?1? , 8 1$ p BA 3?1?8 3$D  p BA 6?1?P 8 6$D  p BA 8?1?P` x8 8$D  p H 1? R  ,$D  N324 = 6b* H p 0޽h ? a( 6 b Z  t( wY t t 3 rtwawa1 ?`    t 3 rwawa1 ?P`<$  ! 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