Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(x^2+16=0\)
- \(7x^2-567=0\)
- \(-5x^2+20=0\)
- \(11x^2+579=7x^2+3\)
- \(8x^2+0=0\)
- \(2x^2+66=5x^2-9\)
- \(7x^2+1372=0\)
- \(3x^2-442=-4x^2+6\)
- \(x^2-16=0\)
- \(-x^2+16=0\)
- \(-4x^2+9=3x^2+9\)
- \(-4(-9x^2+10)=-(-30x^2+190)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(x^2+16=0 \\
\Leftrightarrow x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2-567=0 \\
\Leftrightarrow 7x^2 = 567 \\
\Leftrightarrow x^2 = \frac{567}{7}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-5x^2+20=0 \\
\Leftrightarrow -5x^2 = -20 \\
\Leftrightarrow x^2 = \frac{-20}{-5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(11x^2+579=7x^2+3 \\ \Leftrightarrow 11x^2-7x^2=3-579 \\
\Leftrightarrow 4x^2 = -576 \\
\Leftrightarrow x^2 = \frac{-576}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2+0=0 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2x^2+66=5x^2-9 \\ \Leftrightarrow 2x^2-5x^2=-9-66 \\
\Leftrightarrow -3x^2 = -75 \\
\Leftrightarrow x^2 = \frac{-75}{-3}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(7x^2+1372=0 \\
\Leftrightarrow 7x^2 = -1372 \\
\Leftrightarrow x^2 = \frac{-1372}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2-442=-4x^2+6 \\ \Leftrightarrow 3x^2+4x^2=6+442 \\
\Leftrightarrow 7x^2 = 448 \\
\Leftrightarrow x^2 = \frac{448}{7}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(x^2-16=0 \\
\Leftrightarrow x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{1}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-x^2+16=0 \\
\Leftrightarrow -x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{-1}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-4x^2+9=3x^2+9 \\ \Leftrightarrow -4x^2-3x^2=9-9 \\
\Leftrightarrow -7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-4(-9x^2+10)=-(-30x^2+190) \\ \Leftrightarrow 36x^2-40=30x^2-190 \\
\Leftrightarrow 36x^2-30x^2=-190+40 \\
\Leftrightarrow 6x^2 = -150 \\
\Leftrightarrow x^2 = \frac{-150}{6} < 0 \\
V = \varnothing \\ -----------------\)