Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(8x^2+72=0\)
- \(-16x^2-1007=-10x^2+7\)
- \(2(4x^2+6)=-(-x^2-579)\)
- \(8x^2-32=0\)
- \(2x^2+164=4x^2+2\)
- \(-5x^2-20=0\)
- \(-5x^2+500=0\)
- \(-5x^2-405=0\)
- \(-7x^2+567=0\)
- \(-3x^2+192=0\)
- \(3(9x^2-2)=-(-22x^2-14)\)
- \(-x^2+25=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(8x^2+72=0 \\
\Leftrightarrow 8x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-16x^2-1007=-10x^2+7 \\ \Leftrightarrow -16x^2+10x^2=7+1007 \\
\Leftrightarrow -6x^2 = 1014 \\
\Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(4x^2+6)=-(-x^2-579) \\ \Leftrightarrow 8x^2+12=x^2+579 \\
\Leftrightarrow 8x^2-x^2=579-12 \\
\Leftrightarrow 7x^2 = 567 \\
\Leftrightarrow x^2 = \frac{567}{7}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(8x^2-32=0 \\
\Leftrightarrow 8x^2 = 32 \\
\Leftrightarrow x^2 = \frac{32}{8}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(2x^2+164=4x^2+2 \\ \Leftrightarrow 2x^2-4x^2=2-164 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-5x^2-20=0 \\
\Leftrightarrow -5x^2 = 20 \\
\Leftrightarrow x^2 = \frac{20}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2+500=0 \\
\Leftrightarrow -5x^2 = -500 \\
\Leftrightarrow x^2 = \frac{-500}{-5}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-5x^2-405=0 \\
\Leftrightarrow -5x^2 = 405 \\
\Leftrightarrow x^2 = \frac{405}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2+567=0 \\
\Leftrightarrow -7x^2 = -567 \\
\Leftrightarrow x^2 = \frac{-567}{-7}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-3x^2+192=0 \\
\Leftrightarrow -3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{-3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(3(9x^2-2)=-(-22x^2-14) \\ \Leftrightarrow 27x^2-6=22x^2+14 \\
\Leftrightarrow 27x^2-22x^2=14+6 \\
\Leftrightarrow 5x^2 = 20 \\
\Leftrightarrow x^2 = \frac{20}{5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-x^2+25=0 \\
\Leftrightarrow -x^2 = -25 \\
\Leftrightarrow x^2 = \frac{-25}{-1}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)