# type a/sqrt(bx^2+c)=d
mathviewpanel=$module_title:x=:<=>
!if $rounding=-1
    rounding=0
    !readproc $remarkdir/rounding.$taal
!endif
!if $usage=2
    image=0
!endif
n=$counter
!if $level=0
    R=$counter
!else
    R=$level
!endif

exotext=$empty
keuze=!randitem 1,2
checkfile=exos/checkfile1.proc
!if $subject=15
    varlist=x
    question$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.$taal
    cols=15
    rows=2
    # berekeniningen laten zien
    var3=0
    questiontype=0
    helptext=<a onmouseover="return escape('$helptext')">$sometext</a>
!else
    varlist=x
    # maximaal aantal pijlen=tussenstappenn
    var1=5
    # aantal pijlen=tussenstappen
    var2=3
    # berekeniningen laten zien
    var3=1
    question$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.$taal
    cols=30
    rows=5
    inputs=1
    questiontype=7
    javascript=js/exo1.js
    embed=1
    XSIZE=650                                                                                                                      
    exotext=<a onmouseover="return escape('<img src=$module_dir/gifs/exo16.jpg>')">$sometext</a>
    helptext=$empty
!endif

# question$n = html/ascii vraag
# formula$n  = latex/html versie van de formule
# answer$n = nakijk wiskundige goede antwoorden
# textanswer$n= text/ascii/html versie met uitleg van het goede antwoord
# texanswer$n is latexformule van goede antwoord

!if $R=1
    # type a/sqrt(bx^2-c)=d
    # b=1
    d=!randitem 1,2,3,4,5
    p=!randitem 2,3,4
    a=$[$p*$d]
    c=!randitem 1,2,3,4,5,6,7,8
    pm=!randitem 1,-1
    a=$[$pm*$a]
    d=$[$pm*$d]
    x=$[$p^2+$c]
    test=$[sqrt($x)]
    !if . isin $test
	x1=sqrt($x)
	x2=-sqrt($x)
	x1_tex=\sqrt{$x}
	x2_tex=-\sqrt{$x}
    !else
	x1=$test
	x2=$[-1*$test]
	x1_tex=$x1
	x2_tex=$x2
    !endif
    formula$n=\frac{$a}{\sqrt{x^{2}-$c}}=$d \,\,\rightarrow\,\,	
    tex=$a\,=\,$d \cdot \sqrt{x^{2} - $c} \rightarrow \\ $p=\sqrt{x^{2} - $c} \rightarrow \\ $[$p*$p]=x^{2} - $c \rightarrow \\ $[$p*$p + $c]=x^{2} 
    answer$n=$x1,$x2    
    texanswer$n=\left[ \begin{array}{l} $tex \rightarrow \\  x_{1}=$x1_tex \wedge x_{2}=$x2_tex \end{array}
    
 !exit
!endif

!if $R>1
    # type a/sqrt(bx^2-c)=e/d
    d=!randitem 2,3,4,5,6,7,8,9
    p=!randitem 2,3,4
    e=!randitem 1,2,3,4,5,6,7,8,9
    !if $d=$e
	d=$[$d+1]
    !endif
    a=$[$p*$e]
    c=!randitem 1,2,3,4,5,6,7,8
    b=!randitem 2,3,4,5
    pm=!randitem 1,-1
    a=$[$pm*$a]
    e=$[$pm*$e]
    tot=!exec pari A=((($p)*($d))^2+ ($c))/$b\
    printtex(A)
    x1=!line 1 of $tot
    x1=sqrt($x1)
    x2=-$x1
    x1_tex=!line 2 of $tot
    x1_tex=\sqrt{$x1_tex}
    x2_tex=-$x1_tex
    formula$n=\frac{$a}{\sqrt{$b x^{2}-$c}}= \frac{$e}{$d} \,\,\rightarrow \,\,
    tex=!texmath $[$a*$d] = $e*sqrt($b*x^2 - $c) -> $[$p*$d] = sqrt($b*x^2 - $c) -> $[$p*$d]^2 = $b*x^2 - $c  
    tex=!replace internal \to by $ \rightarrow \\ $ in $tex                                                                                
    texanswer$n=\left[ \begin{array}{l} $tex \rightarrow \\  x_{1}=$x1_tex \wedge x_{2}=$x2_tex \end{array}
    answer$n=$x1,$x2
 !exit
!endif
