Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2(-6x^2-5)=-(-7x^2-190)\)
- \(3x^2+10=2x^2+6\)
- \(x^2-1=0\)
- \(6x^2-726=0\)
- \(-4x^2+400=0\)
- \(5(10x^2+6)=-(-49x^2-14)\)
- \(3(8x^2+7)=-(-26x^2-13)\)
- \(-11x^2+1578=-4x^2+3\)
- \(-4x^2+1158=4x^2+6\)
- \(4(5x^2+7)=-(-27x^2-1036)\)
- \(3x^2+12=0\)
- \(3x^2+134=8x^2+9\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2(-6x^2-5)=-(-7x^2-190) \\ \Leftrightarrow 12x^2+10=7x^2+190 \\
\Leftrightarrow 12x^2-7x^2=190-10 \\
\Leftrightarrow 5x^2 = 180 \\
\Leftrightarrow x^2 = \frac{180}{5}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(3x^2+10=2x^2+6 \\ \Leftrightarrow 3x^2-2x^2=6-10 \\
\Leftrightarrow x^2 = -4 \\
\Leftrightarrow x^2 = \frac{-4}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-1=0 \\
\Leftrightarrow x^2 = 1 \\
\Leftrightarrow x^2 = \frac{1}{1}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(6x^2-726=0 \\
\Leftrightarrow 6x^2 = 726 \\
\Leftrightarrow x^2 = \frac{726}{6}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4x^2+400=0 \\
\Leftrightarrow -4x^2 = -400 \\
\Leftrightarrow x^2 = \frac{-400}{-4}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(5(10x^2+6)=-(-49x^2-14) \\ \Leftrightarrow 50x^2+30=49x^2+14 \\
\Leftrightarrow 50x^2-49x^2=14-30 \\
\Leftrightarrow x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(8x^2+7)=-(-26x^2-13) \\ \Leftrightarrow 24x^2+21=26x^2+13 \\
\Leftrightarrow 24x^2-26x^2=13-21 \\
\Leftrightarrow -2x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{-2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-11x^2+1578=-4x^2+3 \\ \Leftrightarrow -11x^2+4x^2=3-1578 \\
\Leftrightarrow -7x^2 = -1575 \\
\Leftrightarrow x^2 = \frac{-1575}{-7}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-4x^2+1158=4x^2+6 \\ \Leftrightarrow -4x^2-4x^2=6-1158 \\
\Leftrightarrow -8x^2 = -1152 \\
\Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(4(5x^2+7)=-(-27x^2-1036) \\ \Leftrightarrow 20x^2+28=27x^2+1036 \\
\Leftrightarrow 20x^2-27x^2=1036-28 \\
\Leftrightarrow -7x^2 = 1008 \\
\Leftrightarrow x^2 = \frac{1008}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2+12=0 \\
\Leftrightarrow 3x^2 = -12 \\
\Leftrightarrow x^2 = \frac{-12}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2+134=8x^2+9 \\ \Leftrightarrow 3x^2-8x^2=9-134 \\
\Leftrightarrow -5x^2 = -125 \\
\Leftrightarrow x^2 = \frac{-125}{-5}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)