Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2x^2+31=6x^2-5\)
- \(2(9x^2-4)=-(-12x^2-856)\)
- \(3x^2+0=0\)
- \(5(-10x^2-6)=-(53x^2+78)\)
- \(11x^2-578=8x^2+10\)
- \(-4x^2-16=0\)
- \(-6x^2-150=0\)
- \(5(9x^2+7)=-(-40x^2-40)\)
- \(-3x^2+300=0\)
- \(3x^2-105=2x^2-5\)
- \(6x^2-96=0\)
- \(2x^2-392=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2x^2+31=6x^2-5 \\ \Leftrightarrow 2x^2-6x^2=-5-31 \\
\Leftrightarrow -4x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{-4}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(2(9x^2-4)=-(-12x^2-856) \\ \Leftrightarrow 18x^2-8=12x^2+856 \\
\Leftrightarrow 18x^2-12x^2=856+8 \\
\Leftrightarrow 6x^2 = 864 \\
\Leftrightarrow x^2 = \frac{864}{6}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(3x^2+0=0 \\
\Leftrightarrow 3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(-10x^2-6)=-(53x^2+78) \\ \Leftrightarrow -50x^2-30=-53x^2-78 \\
\Leftrightarrow -50x^2+53x^2=-78+30 \\
\Leftrightarrow 3x^2 = -48 \\
\Leftrightarrow x^2 = \frac{-48}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(11x^2-578=8x^2+10 \\ \Leftrightarrow 11x^2-8x^2=10+578 \\
\Leftrightarrow 3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-4x^2-16=0 \\
\Leftrightarrow -4x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-6x^2-150=0 \\
\Leftrightarrow -6x^2 = 150 \\
\Leftrightarrow x^2 = \frac{150}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(9x^2+7)=-(-40x^2-40) \\ \Leftrightarrow 45x^2+35=40x^2+40 \\
\Leftrightarrow 45x^2-40x^2=40-35 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-3x^2+300=0 \\
\Leftrightarrow -3x^2 = -300 \\
\Leftrightarrow x^2 = \frac{-300}{-3}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(3x^2-105=2x^2-5 \\ \Leftrightarrow 3x^2-2x^2=-5+105 \\
\Leftrightarrow x^2 = 100 \\
\Leftrightarrow x^2 = \frac{100}{1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(6x^2-96=0 \\
\Leftrightarrow 6x^2 = 96 \\
\Leftrightarrow x^2 = \frac{96}{6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2x^2-392=0 \\
\Leftrightarrow 2x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{2}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)