Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(x^2-3=4x^2-3\)
- \(7x^2-1008=0\)
- \(3x^2-75=0\)
- \(-4(4x^2-4)=-(10x^2+80)\)
- \(2x^2+288=0\)
- \(-5x^2-80=0\)
- \(-8x^2-86=-9x^2-5\)
- \(-5x^2-180=0\)
- \(-9x^2-31=-8x^2-6\)
- \(5(9x^2+10)=-(-46x^2+94)\)
- \(-8x^2+800=0\)
- \(2x^2+242=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(x^2-3=4x^2-3 \\ \Leftrightarrow x^2-4x^2=-3+3 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(7x^2-1008=0 \\
\Leftrightarrow 7x^2 = 1008 \\
\Leftrightarrow x^2 = \frac{1008}{7}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(3x^2-75=0 \\
\Leftrightarrow 3x^2 = 75 \\
\Leftrightarrow x^2 = \frac{75}{3}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-4(4x^2-4)=-(10x^2+80) \\ \Leftrightarrow -16x^2+16=-10x^2-80 \\
\Leftrightarrow -16x^2+10x^2=-80-16 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2x^2+288=0 \\
\Leftrightarrow 2x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2-80=0 \\
\Leftrightarrow -5x^2 = 80 \\
\Leftrightarrow x^2 = \frac{80}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2-86=-9x^2-5 \\ \Leftrightarrow -8x^2+9x^2=-5+86 \\
\Leftrightarrow x^2 = 81 \\
\Leftrightarrow x^2 = \frac{81}{1}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-5x^2-180=0 \\
\Leftrightarrow -5x^2 = 180 \\
\Leftrightarrow x^2 = \frac{180}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-9x^2-31=-8x^2-6 \\ \Leftrightarrow -9x^2+8x^2=-6+31 \\
\Leftrightarrow -x^2 = 25 \\
\Leftrightarrow x^2 = \frac{25}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(9x^2+10)=-(-46x^2+94) \\ \Leftrightarrow 45x^2+50=46x^2-94 \\
\Leftrightarrow 45x^2-46x^2=-94-50 \\
\Leftrightarrow -x^2 = -144 \\
\Leftrightarrow x^2 = \frac{-144}{-1}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-8x^2+800=0 \\
\Leftrightarrow -8x^2 = -800 \\
\Leftrightarrow x^2 = \frac{-800}{-8}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(2x^2+242=0 \\
\Leftrightarrow 2x^2 = -242 \\
\Leftrightarrow x^2 = \frac{-242}{2} < 0 \\
V = \varnothing \\ -----------------\)