Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(8x^2-12=5x^2-9\)
- \(-3x^2-75=0\)
- \(-6x^2+36=2x^2+4\)
- \(10x^2-33=9x^2-8\)
- \(4x^2+140=10x^2-10\)
- \(6x^2-6=0\)
- \(-2(-7x^2+3)=-(-15x^2-43)\)
- \(x^2-4=0\)
- \(-5x^2+125=0\)
- \(-2(6x^2+8)=-(17x^2-29)\)
- \(5x^2+3=-2x^2+3\)
- \(-2(-8x^2+2)=-(-10x^2-20)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(8x^2-12=5x^2-9 \\ \Leftrightarrow 8x^2-5x^2=-9+12 \\
\Leftrightarrow 3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-3x^2-75=0 \\
\Leftrightarrow -3x^2 = 75 \\
\Leftrightarrow x^2 = \frac{75}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-6x^2+36=2x^2+4 \\ \Leftrightarrow -6x^2-2x^2=4-36 \\
\Leftrightarrow -8x^2 = -32 \\
\Leftrightarrow x^2 = \frac{-32}{-8}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(10x^2-33=9x^2-8 \\ \Leftrightarrow 10x^2-9x^2=-8+33 \\
\Leftrightarrow x^2 = 25 \\
\Leftrightarrow x^2 = \frac{25}{1}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(4x^2+140=10x^2-10 \\ \Leftrightarrow 4x^2-10x^2=-10-140 \\
\Leftrightarrow -6x^2 = -150 \\
\Leftrightarrow x^2 = \frac{-150}{-6}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(6x^2-6=0 \\
\Leftrightarrow 6x^2 = 6 \\
\Leftrightarrow x^2 = \frac{6}{6}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-2(-7x^2+3)=-(-15x^2-43) \\ \Leftrightarrow 14x^2-6=15x^2+43 \\
\Leftrightarrow 14x^2-15x^2=43+6 \\
\Leftrightarrow -x^2 = 49 \\
\Leftrightarrow x^2 = \frac{49}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-4=0 \\
\Leftrightarrow x^2 = 4 \\
\Leftrightarrow x^2 = \frac{4}{1}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-5x^2+125=0 \\
\Leftrightarrow -5x^2 = -125 \\
\Leftrightarrow x^2 = \frac{-125}{-5}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-2(6x^2+8)=-(17x^2-29) \\ \Leftrightarrow -12x^2-16=-17x^2+29 \\
\Leftrightarrow -12x^2+17x^2=29+16 \\
\Leftrightarrow 5x^2 = 45 \\
\Leftrightarrow x^2 = \frac{45}{5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(5x^2+3=-2x^2+3 \\ \Leftrightarrow 5x^2+2x^2=3-3 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2(-8x^2+2)=-(-10x^2-20) \\ \Leftrightarrow 16x^2-4=10x^2+20 \\
\Leftrightarrow 16x^2-10x^2=20+4 \\
\Leftrightarrow 6x^2 = 24 \\
\Leftrightarrow x^2 = \frac{24}{6}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)