Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-6x^2+96=0\)
- \(2(-3x^2-4)=-(0x^2+1358)\)
- \(4(9x^2+3)=-(-43x^2+100)\)
- \(-3(-8x^2+4)=-(-22x^2+12)\)
- \(-4(4x^2+5)=-(18x^2-78)\)
- \(x^2-16=0\)
- \(-4(4x^2+5)=-(14x^2-222)\)
- \(5x^2-80=0\)
- \(-12x^2+22=-9x^2+10\)
- \(-6x^2-600=0\)
- \(2x^2-2=-2x^2-2\)
- \(-3x^2+48=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-6x^2+96=0 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2(-3x^2-4)=-(0x^2+1358) \\ \Leftrightarrow -6x^2-8=0x^2-1358 \\
\Leftrightarrow -6x^2+0x^2=-1358+8 \\
\Leftrightarrow -6x^2 = -1350 \\
\Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(4(9x^2+3)=-(-43x^2+100) \\ \Leftrightarrow 36x^2+12=43x^2-100 \\
\Leftrightarrow 36x^2-43x^2=-100-12 \\
\Leftrightarrow -7x^2 = -112 \\
\Leftrightarrow x^2 = \frac{-112}{-7}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-3(-8x^2+4)=-(-22x^2+12) \\ \Leftrightarrow 24x^2-12=22x^2-12 \\
\Leftrightarrow 24x^2-22x^2=-12+12 \\
\Leftrightarrow 2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-4(4x^2+5)=-(18x^2-78) \\ \Leftrightarrow -16x^2-20=-18x^2+78 \\
\Leftrightarrow -16x^2+18x^2=78+20 \\
\Leftrightarrow 2x^2 = 98 \\
\Leftrightarrow x^2 = \frac{98}{2}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(x^2-16=0 \\
\Leftrightarrow x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{1}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-4(4x^2+5)=-(14x^2-222) \\ \Leftrightarrow -16x^2-20=-14x^2+222 \\
\Leftrightarrow -16x^2+14x^2=222+20 \\
\Leftrightarrow -2x^2 = 242 \\
\Leftrightarrow x^2 = \frac{242}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2-80=0 \\
\Leftrightarrow 5x^2 = 80 \\
\Leftrightarrow x^2 = \frac{80}{5}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-12x^2+22=-9x^2+10 \\ \Leftrightarrow -12x^2+9x^2=10-22 \\
\Leftrightarrow -3x^2 = -12 \\
\Leftrightarrow x^2 = \frac{-12}{-3}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-6x^2-600=0 \\
\Leftrightarrow -6x^2 = 600 \\
\Leftrightarrow x^2 = \frac{600}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2-2=-2x^2-2 \\ \Leftrightarrow 2x^2+2x^2=-2+2 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3x^2+48=0 \\
\Leftrightarrow -3x^2 = -48 \\
\Leftrightarrow x^2 = \frac{-48}{-3}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)