Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2x^2-8=0\)
- \(5x^2-500=0\)
- \(-5x^2+0=0\)
- \(-x^2-2=-8x^2-2\)
- \(-7x^2-112=0\)
- \(-4(-10x^2+9)=-(-39x^2-85)\)
- \(4(9x^2-7)=-(-34x^2-134)\)
- \(-x^2+115=6x^2+3\)
- \(6x^2+216=0\)
- \(-4(3x^2-7)=-(19x^2-140)\)
- \(-8x^2-288=0\)
- \(8x^2+203=9x^2+7\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2x^2-8=0 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(5x^2-500=0 \\
\Leftrightarrow 5x^2 = 500 \\
\Leftrightarrow x^2 = \frac{500}{5}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-5x^2+0=0 \\
\Leftrightarrow -5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-x^2-2=-8x^2-2 \\ \Leftrightarrow -x^2+8x^2=-2+2 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-7x^2-112=0 \\
\Leftrightarrow -7x^2 = 112 \\
\Leftrightarrow x^2 = \frac{112}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-10x^2+9)=-(-39x^2-85) \\ \Leftrightarrow 40x^2-36=39x^2+85 \\
\Leftrightarrow 40x^2-39x^2=85+36 \\
\Leftrightarrow x^2 = 121 \\
\Leftrightarrow x^2 = \frac{121}{1}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(4(9x^2-7)=-(-34x^2-134) \\ \Leftrightarrow 36x^2-28=34x^2+134 \\
\Leftrightarrow 36x^2-34x^2=134+28 \\
\Leftrightarrow 2x^2 = 162 \\
\Leftrightarrow x^2 = \frac{162}{2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-x^2+115=6x^2+3 \\ \Leftrightarrow -x^2-6x^2=3-115 \\
\Leftrightarrow -7x^2 = -112 \\
\Leftrightarrow x^2 = \frac{-112}{-7}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(6x^2+216=0 \\
\Leftrightarrow 6x^2 = -216 \\
\Leftrightarrow x^2 = \frac{-216}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(3x^2-7)=-(19x^2-140) \\ \Leftrightarrow -12x^2+28=-19x^2+140 \\
\Leftrightarrow -12x^2+19x^2=140-28 \\
\Leftrightarrow 7x^2 = 112 \\
\Leftrightarrow x^2 = \frac{112}{7}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-8x^2-288=0 \\
\Leftrightarrow -8x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2+203=9x^2+7 \\ \Leftrightarrow 8x^2-9x^2=7-203 \\
\Leftrightarrow -x^2 = -196 \\
\Leftrightarrow x^2 = \frac{-196}{-1}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)