math=0
questiontype=0
image=0
!set n=$counter
!if $level =0
    R=$counter
!else
    R=$level
!endif        

exotitle=!record 6 of lang/remarks.$taal
#@ Vergelijkingen met Wortels
checkfile=exos/checkfile1.proc
!if $subject=7
    varlist=x
    question$n=!record 1 of lang/remarks.$taal
    #@ Los de volgende vergelijking op:<br>
    sometext=!record 2 of lang/remarks.$taal
    helptext=!record 3 of lang/remarks.$taal
    cols=15
    rows=2
    # berekeniningen laten zien
    var3=0
    helptext=<a onmouseover="return escape('$helptext')">$sometext</a>
!else
    varlist=x
    # maximaal aantal pijlen=tussenstappenn
    var1=5
    # aantal pijlen=tussenstappen
    var2=1
    # berekeniningen laten zien
    var3=1
    question$n=!record 4 of lang/remarks.$taal
    #@ Los de volgende vergelijking op:<br>
    sometext=!record 2 of lang/remarks.$taal
    helptext=!record 5 of lang/remarks.$taal
    cols=25
    rows=5
    inputs=1
    questiontype=7
    javascript=js/exo1.js
    embed=1
    XSIZE=650
    exotext=<a onmouseover="return escape('$helptext')">$sometext</a>
    helptext=$empty
!endif
keuze=!randitem 1,0
!if $R=1
    # sqrt(ax+b)=c => ax+b=c^2 => ax=c^2-b =>  x=(c^2-b)/a 
    d=!randitem 1,4,9,16,25,36,49,64,81,100,121,144
    x=!randint -10,10
    a=!randitem -5,-4,-3,-2,-1,2,3,4,5
    b=$[$d-$a*$x]
    c=$[sqrt($d)]
    #verwijderen van de +-
    tussen=!rawmath x+$b
    formula$n=\sqrt{$a \cdot $tussen} = $c \rightarrow
    texanswer$n=$a \cdot $tussen = $c^{2} \rightarrow $a \cdot x = $[$c^2 -$b]  \rightarrow x=$x
    answer$n=$x
 !exit
!endif 

!if $R=2
    keuze=!randitem 1,2
    # e*sqrt(ax+b)=e*c => ax+b=c^2 => ax=c^2-b =>  x=(c^2-b)/a 
    # e+sqrt(ax+b)=e+c => ax+b=c^2 => ax=c^2-b =>  x=(c^2-b)/a 
    d=!randitem 1,4,9,16,25,36,49,64,81,100,121,144
    x=!randint -10,10
    a=!randitem -5,-4,-3,-2,-1,2,3,4,5
    b=$[$d-$a*$x]
    c=$[sqrt($d)]
    e=!randitem -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9,10
    tussen=!rawmath x+$b
    #verwijderen van de +-
    !if $keuze=1
        f=$[$c*$e]
        formula$n=$e \cdot \sqrt{$a \cdot $tussen} = $f \rightarrow
        texanswer$n=\sqrt{$a \cdot $tussen} = $c \rightarrow $a \cdot $tussen = $c^{2} \rightarrow $a \cdot x = $[$c^2 -$b]  \rightarrow x=$x
    !else
	f=$[$c+$e]
        formula$n=$e + \sqrt{$a \cdot $tussen} = $f \rightarrow
        texanswer$n=\sqrt{$a \cdot $tussen} = $c \rightarrow $a \cdot $tussen = $c^{2} \rightarrow $a \cdot x = $[$c^2 -$b]  \rightarrow x=$x
    !endif
    answer$n=$x
 !exit
!endif 

!if $R=3
    # sqrt(ax+b)=c => ax+b=c^2 => ax=c^2-b =>  x=(c^2-b)/a 
    # sqrt(ax-b)=c => ax-b=c^2 => ax=c^2+b =>  x=(c^2+b)/a 
    a=!randitem -5,-4,-3,-2,-1,2,3,4,5
    b=!randitem 1,2,3,4,5,6,7,8,9,10
    c=!randint 1,10
    !if $keuze=1
        x=$[$c^2-$b]/$a
        formula$n=\sqrt{$a \cdot x + $b} = $c \rightarrow
	tussen=$a \cdot x + $b = $c^{2} \rightarrow $a \cdot x = $[$c^2 -$b]  
    !else
        x=$[$c^2+$b]/$a
        formula$n=\sqrt{$a \cdot x - $b} = $c \rightarrow
	tussen=$a \cdot x - $b = $c^{2} \rightarrow $a \cdot x = $[$c^2 +$b]  
    !endif
    xtex=!exec pari printtex($x)
    texanswer$n=$tussen \rightarrow x=$xtex
    answer$n=$x
 !exit
!endif


!if $R>3
    # e*sqrt(ax+b)=e*c => ax+b=c^2 => ax=c^2-b =>  x=(c^2-b)/a 
    # e+sqrt(ax+b)=e+c => ax+b=c^2 => ax=c^2-b =>  x=(c^2-b)/a 
    a=!randitem -5,-4,-3,-2,-1,2,3,4,5
    b=!randitem 1,2,3,4,5,6,7,8,9,10,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10
    c=!randint 1,10
    d=!randitem -1/7,-1/6,-1/5,-1/4,-1/3,-1/2,1/2,1/3,1/4,1/5,1/6,1/7,1/8,1/9
    pm=!randitem +,-
    tus=!rawmath x+$b
    #verwijderen van de +-
    tot=!exec pari A=($c^2-$b)/$c\
        printtex(A)\
	printtex($d)\
	printtex($d*$c)\
	printtex($d+$c)
    answer$n=!line 1 of $tot
    xtex=!line 2 of $tot
    dtex=!line 3 of $tot
    f1tex=!line 4 of $tot
    f2tex=!line 5 of $tot
    
    !if $keuze=1
        formula$n=$dtex \cdot \sqrt{$a \cdot $tus} = $f1tex  \rightarrow
	tussen=\sqrt{$a \cdot $tus} = $c \rightarrow $a \cdot $tus = $c^{2} \rightarrow $a \cdot x = $[$c^2 -$b]  
    !else
        formula$n=$dtex + \sqrt{$a \cdot $tus} = $f2tex  \rightarrow
	tussen=\sqrt{$a \cdot $tus} = $c \rightarrow $a \cdot $tus = $c^{2}] \rightarrow $a \cdot x = $[$c^2 +$b]  
    !endif
    texanswer$n=$tussen \rightarrow x=$xtex
 !exit
!endif 
#C=!exec pari printtex($a*$b + (1)/$c^2)

