Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(3(-7x^2+7)=-(24x^2-453)\)
- \(4x^2-3=6x^2-3\)
- \(-7x^2+7=0\)
- \(-8x^2+0=0\)
- \(-5(10x^2+4)=-(46x^2+20)\)
- \(-5x^2-153=-4x^2-9\)
- \(-4(-6x^2+9)=-(-19x^2-284)\)
- \(x^2-36=0\)
- \(-3x^2-3=2x^2-3\)
- \(-6x^2+390=-4x^2-2\)
- \(16x^2+110=9x^2-2\)
- \(17x^2-6=9x^2+2\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(3(-7x^2+7)=-(24x^2-453) \\ \Leftrightarrow -21x^2+21=-24x^2+453 \\
\Leftrightarrow -21x^2+24x^2=453-21 \\
\Leftrightarrow 3x^2 = 432 \\
\Leftrightarrow x^2 = \frac{432}{3}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(4x^2-3=6x^2-3 \\ \Leftrightarrow 4x^2-6x^2=-3+3 \\
\Leftrightarrow -2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-7x^2+7=0 \\
\Leftrightarrow -7x^2 = -7 \\
\Leftrightarrow x^2 = \frac{-7}{-7}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5(10x^2+4)=-(46x^2+20) \\ \Leftrightarrow -50x^2-20=-46x^2-20 \\
\Leftrightarrow -50x^2+46x^2=-20+20 \\
\Leftrightarrow -4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5x^2-153=-4x^2-9 \\ \Leftrightarrow -5x^2+4x^2=-9+153 \\
\Leftrightarrow -x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-6x^2+9)=-(-19x^2-284) \\ \Leftrightarrow 24x^2-36=19x^2+284 \\
\Leftrightarrow 24x^2-19x^2=284+36 \\
\Leftrightarrow 5x^2 = 320 \\
\Leftrightarrow x^2 = \frac{320}{5}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(x^2-36=0 \\
\Leftrightarrow x^2 = 36 \\
\Leftrightarrow x^2 = \frac{36}{1}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-3x^2-3=2x^2-3 \\ \Leftrightarrow -3x^2-2x^2=-3+3 \\
\Leftrightarrow -5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-6x^2+390=-4x^2-2 \\ \Leftrightarrow -6x^2+4x^2=-2-390 \\
\Leftrightarrow -2x^2 = -392 \\
\Leftrightarrow x^2 = \frac{-392}{-2}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(16x^2+110=9x^2-2 \\ \Leftrightarrow 16x^2-9x^2=-2-110 \\
\Leftrightarrow 7x^2 = -112 \\
\Leftrightarrow x^2 = \frac{-112}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(17x^2-6=9x^2+2 \\ \Leftrightarrow 17x^2-9x^2=2+6 \\
\Leftrightarrow 8x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{8}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)