Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(8x^2-1800=0\)
- \(8x^2-8=0\)
- \(5x^2+83=6x^2+2\)
- \(3(4x^2+10)=-(-9x^2-30)\)
- \(2x^2-242=0\)
- \(3(-7x^2+8)=-(17x^2+40)\)
- \(6x^2+1014=0\)
- \(5x^2+69=6x^2+5\)
- \(2x^2+109=9x^2-3\)
- \(-14x^2+88=-8x^2-8\)
- \(-5x^2-183=-10x^2-3\)
- \(-x^2+9=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(8x^2-1800=0 \\
\Leftrightarrow 8x^2 = 1800 \\
\Leftrightarrow x^2 = \frac{1800}{8}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(8x^2-8=0 \\
\Leftrightarrow 8x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{8}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(5x^2+83=6x^2+2 \\ \Leftrightarrow 5x^2-6x^2=2-83 \\
\Leftrightarrow -x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{-1}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(3(4x^2+10)=-(-9x^2-30) \\ \Leftrightarrow 12x^2+30=9x^2+30 \\
\Leftrightarrow 12x^2-9x^2=30-30 \\
\Leftrightarrow 3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2x^2-242=0 \\
\Leftrightarrow 2x^2 = 242 \\
\Leftrightarrow x^2 = \frac{242}{2}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(3(-7x^2+8)=-(17x^2+40) \\ \Leftrightarrow -21x^2+24=-17x^2-40 \\
\Leftrightarrow -21x^2+17x^2=-40-24 \\
\Leftrightarrow -4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(6x^2+1014=0 \\
\Leftrightarrow 6x^2 = -1014 \\
\Leftrightarrow x^2 = \frac{-1014}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2+69=6x^2+5 \\ \Leftrightarrow 5x^2-6x^2=5-69 \\
\Leftrightarrow -x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-1}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(2x^2+109=9x^2-3 \\ \Leftrightarrow 2x^2-9x^2=-3-109 \\
\Leftrightarrow -7x^2 = -112 \\
\Leftrightarrow x^2 = \frac{-112}{-7}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-14x^2+88=-8x^2-8 \\ \Leftrightarrow -14x^2+8x^2=-8-88 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-5x^2-183=-10x^2-3 \\ \Leftrightarrow -5x^2+10x^2=-3+183 \\
\Leftrightarrow 5x^2 = 180 \\
\Leftrightarrow x^2 = \frac{180}{5}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-x^2+9=0 \\
\Leftrightarrow -x^2 = -9 \\
\Leftrightarrow x^2 = \frac{-9}{-1}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)