Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(8x^2+0=0\)
- \(9x^2-7=6x^2-4\)
- \(2(2x^2+7)=-(-7x^2+94)\)
- \(2(7x^2-2)=-(-6x^2-196)\)
- \(-2x^2+9=2x^2+9\)
- \(5(-4x^2-8)=-(28x^2-472)\)
- \(-2(-9x^2-7)=-(-17x^2-10)\)
- \(5(-4x^2+9)=-(18x^2+5)\)
- \(-3x^2+22=2x^2+2\)
- \(-5x^2+720=0\)
- \(-3(10x^2+3)=-(35x^2-596)\)
- \(6x^2-486=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(8x^2+0=0 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(9x^2-7=6x^2-4 \\ \Leftrightarrow 9x^2-6x^2=-4+7 \\
\Leftrightarrow 3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(2(2x^2+7)=-(-7x^2+94) \\ \Leftrightarrow 4x^2+14=7x^2-94 \\
\Leftrightarrow 4x^2-7x^2=-94-14 \\
\Leftrightarrow -3x^2 = -108 \\
\Leftrightarrow x^2 = \frac{-108}{-3}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(2(7x^2-2)=-(-6x^2-196) \\ \Leftrightarrow 14x^2-4=6x^2+196 \\
\Leftrightarrow 14x^2-6x^2=196+4 \\
\Leftrightarrow 8x^2 = 200 \\
\Leftrightarrow x^2 = \frac{200}{8}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-2x^2+9=2x^2+9 \\ \Leftrightarrow -2x^2-2x^2=9-9 \\
\Leftrightarrow -4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(-4x^2-8)=-(28x^2-472) \\ \Leftrightarrow -20x^2-40=-28x^2+472 \\
\Leftrightarrow -20x^2+28x^2=472+40 \\
\Leftrightarrow 8x^2 = 512 \\
\Leftrightarrow x^2 = \frac{512}{8}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-2(-9x^2-7)=-(-17x^2-10) \\ \Leftrightarrow 18x^2+14=17x^2+10 \\
\Leftrightarrow 18x^2-17x^2=10-14 \\
\Leftrightarrow x^2 = -4 \\
\Leftrightarrow x^2 = \frac{-4}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(-4x^2+9)=-(18x^2+5) \\ \Leftrightarrow -20x^2+45=-18x^2-5 \\
\Leftrightarrow -20x^2+18x^2=-5-45 \\
\Leftrightarrow -2x^2 = -50 \\
\Leftrightarrow x^2 = \frac{-50}{-2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-3x^2+22=2x^2+2 \\ \Leftrightarrow -3x^2-2x^2=2-22 \\
\Leftrightarrow -5x^2 = -20 \\
\Leftrightarrow x^2 = \frac{-20}{-5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-5x^2+720=0 \\
\Leftrightarrow -5x^2 = -720 \\
\Leftrightarrow x^2 = \frac{-720}{-5}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-3(10x^2+3)=-(35x^2-596) \\ \Leftrightarrow -30x^2-9=-35x^2+596 \\
\Leftrightarrow -30x^2+35x^2=596+9 \\
\Leftrightarrow 5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(6x^2-486=0 \\
\Leftrightarrow 6x^2 = 486 \\
\Leftrightarrow x^2 = \frac{486}{6}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)