Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-8x^2+0=0\)
- \(-2(-9x^2+5)=-(-21x^2+7)\)
- \(2(5x^2-7)=-(-8x^2+12)\)
- \(-8x^2+1152=0\)
- \(-4x^2+324=0\)
- \(4x^2+5=3x^2+4\)
- \(12x^2+29=4x^2-3\)
- \(3x^2-363=0\)
- \(9x^2-38=4x^2+7\)
- \(-4x^2+64=0\)
- \(2x^2+209=-4x^2-7\)
- \(-5x^2+180=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2(-9x^2+5)=-(-21x^2+7) \\ \Leftrightarrow 18x^2-10=21x^2-7 \\
\Leftrightarrow 18x^2-21x^2=-7+10 \\
\Leftrightarrow -3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(5x^2-7)=-(-8x^2+12) \\ \Leftrightarrow 10x^2-14=8x^2-12 \\
\Leftrightarrow 10x^2-8x^2=-12+14 \\
\Leftrightarrow 2x^2 = 2 \\
\Leftrightarrow x^2 = \frac{2}{2}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-8x^2+1152=0 \\
\Leftrightarrow -8x^2 = -1152 \\
\Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-4x^2+324=0 \\
\Leftrightarrow -4x^2 = -324 \\
\Leftrightarrow x^2 = \frac{-324}{-4}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(4x^2+5=3x^2+4 \\ \Leftrightarrow 4x^2-3x^2=4-5 \\
\Leftrightarrow x^2 = -1 \\
\Leftrightarrow x^2 = \frac{-1}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(12x^2+29=4x^2-3 \\ \Leftrightarrow 12x^2-4x^2=-3-29 \\
\Leftrightarrow 8x^2 = -32 \\
\Leftrightarrow x^2 = \frac{-32}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(3x^2-363=0 \\
\Leftrightarrow 3x^2 = 363 \\
\Leftrightarrow x^2 = \frac{363}{3}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(9x^2-38=4x^2+7 \\ \Leftrightarrow 9x^2-4x^2=7+38 \\
\Leftrightarrow 5x^2 = 45 \\
\Leftrightarrow x^2 = \frac{45}{5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-4x^2+64=0 \\
\Leftrightarrow -4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2x^2+209=-4x^2-7 \\ \Leftrightarrow 2x^2+4x^2=-7-209 \\
\Leftrightarrow 6x^2 = -216 \\
\Leftrightarrow x^2 = \frac{-216}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2+180=0 \\
\Leftrightarrow -5x^2 = -180 \\
\Leftrightarrow x^2 = \frac{-180}{-5}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)