Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(3(7x^2+5)=-(-29x^2-983)\)
- \(5(6x^2-2)=-(-26x^2+74)\)
- \(-2x^2+28=-3x^2+3\)
- \(-11x^2+608=-5x^2+8\)
- \(-5x^2-605=0\)
- \(9x^2-93=5x^2+7\)
- \(-3(-6x^2-8)=-(-21x^2+219)\)
- \(-x^2-9=0\)
- \(5(10x^2+6)=-(-46x^2+454)\)
- \(-2(-10x^2+3)=-(-12x^2+654)\)
- \(13x^2-7=8x^2-7\)
- \(-2(-6x^2+6)=-(-7x^2-68)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(3(7x^2+5)=-(-29x^2-983) \\ \Leftrightarrow 21x^2+15=29x^2+983 \\
\Leftrightarrow 21x^2-29x^2=983-15 \\
\Leftrightarrow -8x^2 = 968 \\
\Leftrightarrow x^2 = \frac{968}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(6x^2-2)=-(-26x^2+74) \\ \Leftrightarrow 30x^2-10=26x^2-74 \\
\Leftrightarrow 30x^2-26x^2=-74+10 \\
\Leftrightarrow 4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2+28=-3x^2+3 \\ \Leftrightarrow -2x^2+3x^2=3-28 \\
\Leftrightarrow x^2 = -25 \\
\Leftrightarrow x^2 = \frac{-25}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2+608=-5x^2+8 \\ \Leftrightarrow -11x^2+5x^2=8-608 \\
\Leftrightarrow -6x^2 = -600 \\
\Leftrightarrow x^2 = \frac{-600}{-6}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-5x^2-605=0 \\
\Leftrightarrow -5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(9x^2-93=5x^2+7 \\ \Leftrightarrow 9x^2-5x^2=7+93 \\
\Leftrightarrow 4x^2 = 100 \\
\Leftrightarrow x^2 = \frac{100}{4}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-3(-6x^2-8)=-(-21x^2+219) \\ \Leftrightarrow 18x^2+24=21x^2-219 \\
\Leftrightarrow 18x^2-21x^2=-219-24 \\
\Leftrightarrow -3x^2 = -243 \\
\Leftrightarrow x^2 = \frac{-243}{-3}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-x^2-9=0 \\
\Leftrightarrow -x^2 = 9 \\
\Leftrightarrow x^2 = \frac{9}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(10x^2+6)=-(-46x^2+454) \\ \Leftrightarrow 50x^2+30=46x^2-454 \\
\Leftrightarrow 50x^2-46x^2=-454-30 \\
\Leftrightarrow 4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2(-10x^2+3)=-(-12x^2+654) \\ \Leftrightarrow 20x^2-6=12x^2-654 \\
\Leftrightarrow 20x^2-12x^2=-654+6 \\
\Leftrightarrow 8x^2 = -648 \\
\Leftrightarrow x^2 = \frac{-648}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(13x^2-7=8x^2-7 \\ \Leftrightarrow 13x^2-8x^2=-7+7 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2(-6x^2+6)=-(-7x^2-68) \\ \Leftrightarrow 12x^2-12=7x^2+68 \\
\Leftrightarrow 12x^2-7x^2=68+12 \\
\Leftrightarrow 5x^2 = 80 \\
\Leftrightarrow x^2 = \frac{80}{5}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)