Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(3x^2-75=0\)
- \(8x^2+72=0\)
- \(5x^2-720=0\)
- \(6x^2-266=2x^2-10\)
- \(-3x^2+300=0\)
- \(2(-9x^2+5)=-(25x^2-185)\)
- \(-6x^2-36=-8x^2-4\)
- \(-5x^2+3=-6x^2+4\)
- \(-3x^2+108=0\)
- \(5x^2-605=0\)
- \(-3x^2+48=0\)
- \(-5(-3x^2+9)=-(-10x^2-80)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(3x^2-75=0 \\
\Leftrightarrow 3x^2 = 75 \\
\Leftrightarrow x^2 = \frac{75}{3}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(8x^2+72=0 \\
\Leftrightarrow 8x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2-720=0 \\
\Leftrightarrow 5x^2 = 720 \\
\Leftrightarrow x^2 = \frac{720}{5}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(6x^2-266=2x^2-10 \\ \Leftrightarrow 6x^2-2x^2=-10+266 \\
\Leftrightarrow 4x^2 = 256 \\
\Leftrightarrow x^2 = \frac{256}{4}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-3x^2+300=0 \\
\Leftrightarrow -3x^2 = -300 \\
\Leftrightarrow x^2 = \frac{-300}{-3}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(2(-9x^2+5)=-(25x^2-185) \\ \Leftrightarrow -18x^2+10=-25x^2+185 \\
\Leftrightarrow -18x^2+25x^2=185-10 \\
\Leftrightarrow 7x^2 = 175 \\
\Leftrightarrow x^2 = \frac{175}{7}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-6x^2-36=-8x^2-4 \\ \Leftrightarrow -6x^2+8x^2=-4+36 \\
\Leftrightarrow 2x^2 = 32 \\
\Leftrightarrow x^2 = \frac{32}{2}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-5x^2+3=-6x^2+4 \\ \Leftrightarrow -5x^2+6x^2=4-3 \\
\Leftrightarrow x^2 = 1 \\
\Leftrightarrow x^2 = \frac{1}{1}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-3x^2+108=0 \\
\Leftrightarrow -3x^2 = -108 \\
\Leftrightarrow x^2 = \frac{-108}{-3}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(5x^2-605=0 \\
\Leftrightarrow 5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-3x^2+48=0 \\
\Leftrightarrow -3x^2 = -48 \\
\Leftrightarrow x^2 = \frac{-48}{-3}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-5(-3x^2+9)=-(-10x^2-80) \\ \Leftrightarrow 15x^2-45=10x^2+80 \\
\Leftrightarrow 15x^2-10x^2=80+45 \\
\Leftrightarrow 5x^2 = 125 \\
\Leftrightarrow x^2 = \frac{125}{5}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)