Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2x^2-450=0\)
- \(-5(-5x^2+5)=-(-22x^2+22)\)
- \(2(10x^2-9)=-(-19x^2-46)\)
- \(x^2-792=5x^2-8\)
- \(-6x^2+1350=0\)
- \(4(-8x^2+6)=-(30x^2+138)\)
- \(-3(-8x^2-4)=-(-31x^2-859)\)
- \(6x^2+216=0\)
- \(-2x^2-450=0\)
- \(3x^2-192=0\)
- \(2x^2+72=0\)
- \(4x^2-100=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2x^2-450=0 \\
\Leftrightarrow 2x^2 = 450 \\
\Leftrightarrow x^2 = \frac{450}{2}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-5(-5x^2+5)=-(-22x^2+22) \\ \Leftrightarrow 25x^2-25=22x^2-22 \\
\Leftrightarrow 25x^2-22x^2=-22+25 \\
\Leftrightarrow 3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(2(10x^2-9)=-(-19x^2-46) \\ \Leftrightarrow 20x^2-18=19x^2+46 \\
\Leftrightarrow 20x^2-19x^2=46+18 \\
\Leftrightarrow x^2 = 64 \\
\Leftrightarrow x^2 = \frac{64}{1}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(x^2-792=5x^2-8 \\ \Leftrightarrow x^2-5x^2=-8+792 \\
\Leftrightarrow -4x^2 = 784 \\
\Leftrightarrow x^2 = \frac{784}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-6x^2+1350=0 \\
\Leftrightarrow -6x^2 = -1350 \\
\Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(4(-8x^2+6)=-(30x^2+138) \\ \Leftrightarrow -32x^2+24=-30x^2-138 \\
\Leftrightarrow -32x^2+30x^2=-138-24 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-3(-8x^2-4)=-(-31x^2-859) \\ \Leftrightarrow 24x^2+12=31x^2+859 \\
\Leftrightarrow 24x^2-31x^2=859-12 \\
\Leftrightarrow -7x^2 = 847 \\
\Leftrightarrow x^2 = \frac{847}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2+216=0 \\
\Leftrightarrow 6x^2 = -216 \\
\Leftrightarrow x^2 = \frac{-216}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2-450=0 \\
\Leftrightarrow -2x^2 = 450 \\
\Leftrightarrow x^2 = \frac{450}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2-192=0 \\
\Leftrightarrow 3x^2 = 192 \\
\Leftrightarrow x^2 = \frac{192}{3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(2x^2+72=0 \\
\Leftrightarrow 2x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2-100=0 \\
\Leftrightarrow 4x^2 = 100 \\
\Leftrightarrow x^2 = \frac{100}{4}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)