Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4x^2-100=0\)
- \(4(5x^2-7)=-(-12x^2+36)\)
- \(3x^2+108=0\)
- \(6x^2-5=2x^2-5\)
- \(-9x^2+290=-6x^2-10\)
- \(-x^2+49=0\)
- \(-4x^2-676=0\)
- \(4(8x^2-3)=-(-34x^2+174)\)
- \(-x^2+0=0\)
- \(-8x^2+968=0\)
- \(-9x^2-5=-10x^2+4\)
- \(-5(-4x^2-10)=-(-25x^2+795)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4x^2-100=0 \\
\Leftrightarrow 4x^2 = 100 \\
\Leftrightarrow x^2 = \frac{100}{4}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(4(5x^2-7)=-(-12x^2+36) \\ \Leftrightarrow 20x^2-28=12x^2-36 \\
\Leftrightarrow 20x^2-12x^2=-36+28 \\
\Leftrightarrow 8x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2+108=0 \\
\Leftrightarrow 3x^2 = -108 \\
\Leftrightarrow x^2 = \frac{-108}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-5=2x^2-5 \\ \Leftrightarrow 6x^2-2x^2=-5+5 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-9x^2+290=-6x^2-10 \\ \Leftrightarrow -9x^2+6x^2=-10-290 \\
\Leftrightarrow -3x^2 = -300 \\
\Leftrightarrow x^2 = \frac{-300}{-3}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-x^2+49=0 \\
\Leftrightarrow -x^2 = -49 \\
\Leftrightarrow x^2 = \frac{-49}{-1}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-4x^2-676=0 \\
\Leftrightarrow -4x^2 = 676 \\
\Leftrightarrow x^2 = \frac{676}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(8x^2-3)=-(-34x^2+174) \\ \Leftrightarrow 32x^2-12=34x^2-174 \\
\Leftrightarrow 32x^2-34x^2=-174+12 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-x^2+0=0 \\
\Leftrightarrow -x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-8x^2+968=0 \\
\Leftrightarrow -8x^2 = -968 \\
\Leftrightarrow x^2 = \frac{-968}{-8}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-9x^2-5=-10x^2+4 \\ \Leftrightarrow -9x^2+10x^2=4+5 \\
\Leftrightarrow x^2 = 9 \\
\Leftrightarrow x^2 = \frac{9}{1}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-5(-4x^2-10)=-(-25x^2+795) \\ \Leftrightarrow 20x^2+50=25x^2-795 \\
\Leftrightarrow 20x^2-25x^2=-795-50 \\
\Leftrightarrow -5x^2 = -845 \\
\Leftrightarrow x^2 = \frac{-845}{-5}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)