Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(9x^2+610=4x^2+5\)
- \(-11x^2+259=-7x^2+3\)
- \(5(2x^2+5)=-(-17x^2+150)\)
- \(-11x^2+74=-10x^2+10\)
- \(5x^2-20=0\)
- \(7x^2-252=0\)
- \(-4x^2+836=-9x^2-9\)
- \(-5(10x^2-8)=-(45x^2+565)\)
- \(14x^2-10=8x^2-4\)
- \(2x^2-128=0\)
- \(-5(-6x^2-5)=-(-25x^2-25)\)
- \(2x^2-5=7x^2-10\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(9x^2+610=4x^2+5 \\ \Leftrightarrow 9x^2-4x^2=5-610 \\
\Leftrightarrow 5x^2 = -605 \\
\Leftrightarrow x^2 = \frac{-605}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2+259=-7x^2+3 \\ \Leftrightarrow -11x^2+7x^2=3-259 \\
\Leftrightarrow -4x^2 = -256 \\
\Leftrightarrow x^2 = \frac{-256}{-4}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(5(2x^2+5)=-(-17x^2+150) \\ \Leftrightarrow 10x^2+25=17x^2-150 \\
\Leftrightarrow 10x^2-17x^2=-150-25 \\
\Leftrightarrow -7x^2 = -175 \\
\Leftrightarrow x^2 = \frac{-175}{-7}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-11x^2+74=-10x^2+10 \\ \Leftrightarrow -11x^2+10x^2=10-74 \\
\Leftrightarrow -x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-1}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(5x^2-20=0 \\
\Leftrightarrow 5x^2 = 20 \\
\Leftrightarrow x^2 = \frac{20}{5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(7x^2-252=0 \\
\Leftrightarrow 7x^2 = 252 \\
\Leftrightarrow x^2 = \frac{252}{7}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-4x^2+836=-9x^2-9 \\ \Leftrightarrow -4x^2+9x^2=-9-836 \\
\Leftrightarrow 5x^2 = -845 \\
\Leftrightarrow x^2 = \frac{-845}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(10x^2-8)=-(45x^2+565) \\ \Leftrightarrow -50x^2+40=-45x^2-565 \\
\Leftrightarrow -50x^2+45x^2=-565-40 \\
\Leftrightarrow -5x^2 = -605 \\
\Leftrightarrow x^2 = \frac{-605}{-5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(14x^2-10=8x^2-4 \\ \Leftrightarrow 14x^2-8x^2=-4+10 \\
\Leftrightarrow 6x^2 = 6 \\
\Leftrightarrow x^2 = \frac{6}{6}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(2x^2-128=0 \\
\Leftrightarrow 2x^2 = 128 \\
\Leftrightarrow x^2 = \frac{128}{2}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-5(-6x^2-5)=-(-25x^2-25) \\ \Leftrightarrow 30x^2+25=25x^2+25 \\
\Leftrightarrow 30x^2-25x^2=25-25 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2x^2-5=7x^2-10 \\ \Leftrightarrow 2x^2-7x^2=-10+5 \\
\Leftrightarrow -5x^2 = -5 \\
\Leftrightarrow x^2 = \frac{-5}{-5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)