Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2x^2+0=0\)
- \(3x^2-12=0\)
- \(x^2+31=-3x^2-5\)
- \(8x^2-1352=0\)
- \(-5x^2-605=0\)
- \(-8x^2+47=-3x^2+2\)
- \(4(-6x^2+3)=-(16x^2+276)\)
- \(7x^2-1372=0\)
- \(-6x^2-294=0\)
- \(-2(-6x^2-3)=-(-10x^2-24)\)
- \(-3x^2-729=2x^2-9\)
- \(4x^2+0=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2x^2+0=0 \\
\Leftrightarrow -2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(3x^2-12=0 \\
\Leftrightarrow 3x^2 = 12 \\
\Leftrightarrow x^2 = \frac{12}{3}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(x^2+31=-3x^2-5 \\ \Leftrightarrow x^2+3x^2=-5-31 \\
\Leftrightarrow 4x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2-1352=0 \\
\Leftrightarrow 8x^2 = 1352 \\
\Leftrightarrow x^2 = \frac{1352}{8}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-5x^2-605=0 \\
\Leftrightarrow -5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+47=-3x^2+2 \\ \Leftrightarrow -8x^2+3x^2=2-47 \\
\Leftrightarrow -5x^2 = -45 \\
\Leftrightarrow x^2 = \frac{-45}{-5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(4(-6x^2+3)=-(16x^2+276) \\ \Leftrightarrow -24x^2+12=-16x^2-276 \\
\Leftrightarrow -24x^2+16x^2=-276-12 \\
\Leftrightarrow -8x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{-8}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(7x^2-1372=0 \\
\Leftrightarrow 7x^2 = 1372 \\
\Leftrightarrow x^2 = \frac{1372}{7}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-6x^2-294=0 \\
\Leftrightarrow -6x^2 = 294 \\
\Leftrightarrow x^2 = \frac{294}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2(-6x^2-3)=-(-10x^2-24) \\ \Leftrightarrow 12x^2+6=10x^2+24 \\
\Leftrightarrow 12x^2-10x^2=24-6 \\
\Leftrightarrow 2x^2 = 18 \\
\Leftrightarrow x^2 = \frac{18}{2}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-3x^2-729=2x^2-9 \\ \Leftrightarrow -3x^2-2x^2=-9+729 \\
\Leftrightarrow -5x^2 = 720 \\
\Leftrightarrow x^2 = \frac{720}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2+0=0 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)