Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-8x^2+128=0\)
- \(-3(-7x^2+7)=-(-16x^2-959)\)
- \(-4(8x^2+9)=-(37x^2-284)\)
- \(-4(10x^2-10)=-(37x^2-40)\)
- \(-2(-8x^2-4)=-(-10x^2-8)\)
- \(-7x^2+0=0\)
- \(5(10x^2-3)=-(-45x^2+15)\)
- \(-6x^2-216=0\)
- \(3(8x^2-4)=-(-21x^2-135)\)
- \(4(-10x^2-5)=-(39x^2+69)\)
- \(5x^2-125=0\)
- \(-6x^2+1350=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-8x^2+128=0 \\
\Leftrightarrow -8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-8}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-3(-7x^2+7)=-(-16x^2-959) \\ \Leftrightarrow 21x^2-21=16x^2+959 \\
\Leftrightarrow 21x^2-16x^2=959+21 \\
\Leftrightarrow 5x^2 = 980 \\
\Leftrightarrow x^2 = \frac{980}{5}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-4(8x^2+9)=-(37x^2-284) \\ \Leftrightarrow -32x^2-36=-37x^2+284 \\
\Leftrightarrow -32x^2+37x^2=284+36 \\
\Leftrightarrow 5x^2 = 320 \\
\Leftrightarrow x^2 = \frac{320}{5}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-4(10x^2-10)=-(37x^2-40) \\ \Leftrightarrow -40x^2+40=-37x^2+40 \\
\Leftrightarrow -40x^2+37x^2=40-40 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2(-8x^2-4)=-(-10x^2-8) \\ \Leftrightarrow 16x^2+8=10x^2+8 \\
\Leftrightarrow 16x^2-10x^2=8-8 \\
\Leftrightarrow 6x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{6}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-7x^2+0=0 \\
\Leftrightarrow -7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(10x^2-3)=-(-45x^2+15) \\ \Leftrightarrow 50x^2-15=45x^2-15 \\
\Leftrightarrow 50x^2-45x^2=-15+15 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-6x^2-216=0 \\
\Leftrightarrow -6x^2 = 216 \\
\Leftrightarrow x^2 = \frac{216}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(8x^2-4)=-(-21x^2-135) \\ \Leftrightarrow 24x^2-12=21x^2+135 \\
\Leftrightarrow 24x^2-21x^2=135+12 \\
\Leftrightarrow 3x^2 = 147 \\
\Leftrightarrow x^2 = \frac{147}{3}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(4(-10x^2-5)=-(39x^2+69) \\ \Leftrightarrow -40x^2-20=-39x^2-69 \\
\Leftrightarrow -40x^2+39x^2=-69+20 \\
\Leftrightarrow -x^2 = -49 \\
\Leftrightarrow x^2 = \frac{-49}{-1}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(5x^2-125=0 \\
\Leftrightarrow 5x^2 = 125 \\
\Leftrightarrow x^2 = \frac{125}{5}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-6x^2+1350=0 \\
\Leftrightarrow -6x^2 = -1350 \\
\Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)