Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(3x^2+6=8x^2+6\)
- \(-3(8x^2+8)=-(21x^2-84)\)
- \(-5(5x^2-9)=-(27x^2-437)\)
- \(8x^2+0=0\)
- \(-5x^2-605=0\)
- \(5(-2x^2-6)=-(16x^2-186)\)
- \(6x^2+24=0\)
- \(11x^2-595=6x^2+10\)
- \(11x^2-849=4x^2-2\)
- \(-3(-9x^2-10)=-(-24x^2+45)\)
- \(-10x^2-656=-2x^2-8\)
- \(-4x^2+400=-9x^2-5\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(3x^2+6=8x^2+6 \\ \Leftrightarrow 3x^2-8x^2=6-6 \\
\Leftrightarrow -5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3(8x^2+8)=-(21x^2-84) \\ \Leftrightarrow -24x^2-24=-21x^2+84 \\
\Leftrightarrow -24x^2+21x^2=84+24 \\
\Leftrightarrow -3x^2 = 108 \\
\Leftrightarrow x^2 = \frac{108}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5(5x^2-9)=-(27x^2-437) \\ \Leftrightarrow -25x^2+45=-27x^2+437 \\
\Leftrightarrow -25x^2+27x^2=437-45 \\
\Leftrightarrow 2x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{2}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(8x^2+0=0 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5x^2-605=0 \\
\Leftrightarrow -5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(-2x^2-6)=-(16x^2-186) \\ \Leftrightarrow -10x^2-30=-16x^2+186 \\
\Leftrightarrow -10x^2+16x^2=186+30 \\
\Leftrightarrow 6x^2 = 216 \\
\Leftrightarrow x^2 = \frac{216}{6}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(6x^2+24=0 \\
\Leftrightarrow 6x^2 = -24 \\
\Leftrightarrow x^2 = \frac{-24}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(11x^2-595=6x^2+10 \\ \Leftrightarrow 11x^2-6x^2=10+595 \\
\Leftrightarrow 5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(11x^2-849=4x^2-2 \\ \Leftrightarrow 11x^2-4x^2=-2+849 \\
\Leftrightarrow 7x^2 = 847 \\
\Leftrightarrow x^2 = \frac{847}{7}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-3(-9x^2-10)=-(-24x^2+45) \\ \Leftrightarrow 27x^2+30=24x^2-45 \\
\Leftrightarrow 27x^2-24x^2=-45-30 \\
\Leftrightarrow 3x^2 = -75 \\
\Leftrightarrow x^2 = \frac{-75}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-10x^2-656=-2x^2-8 \\ \Leftrightarrow -10x^2+2x^2=-8+656 \\
\Leftrightarrow -8x^2 = 648 \\
\Leftrightarrow x^2 = \frac{648}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2+400=-9x^2-5 \\ \Leftrightarrow -4x^2+9x^2=-5-400 \\
\Leftrightarrow 5x^2 = -405 \\
\Leftrightarrow x^2 = \frac{-405}{5} < 0 \\
V = \varnothing \\ -----------------\)