Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4x^2-144=0\)
- \(x^2+300=7x^2+6\)
- \(-7x^2+89=-2x^2+9\)
- \(-3(8x^2+3)=-(20x^2+45)\)
- \(-7x^2+11=-2x^2-9\)
- \(3(-7x^2+7)=-(20x^2+175)\)
- \(2x^2-8=0\)
- \(3(2x^2-3)=-(-14x^2+81)\)
- \(7x^2+15=8x^2+6\)
- \(-x^2-503=4x^2-3\)
- \(-5x^2-193=-3x^2+7\)
- \(-8x^2+0=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4x^2-144=0 \\
\Leftrightarrow 4x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{4}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(x^2+300=7x^2+6 \\ \Leftrightarrow x^2-7x^2=6-300 \\
\Leftrightarrow -6x^2 = -294 \\
\Leftrightarrow x^2 = \frac{-294}{-6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-7x^2+89=-2x^2+9 \\ \Leftrightarrow -7x^2+2x^2=9-89 \\
\Leftrightarrow -5x^2 = -80 \\
\Leftrightarrow x^2 = \frac{-80}{-5}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-3(8x^2+3)=-(20x^2+45) \\ \Leftrightarrow -24x^2-9=-20x^2-45 \\
\Leftrightarrow -24x^2+20x^2=-45+9 \\
\Leftrightarrow -4x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{-4}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-7x^2+11=-2x^2-9 \\ \Leftrightarrow -7x^2+2x^2=-9-11 \\
\Leftrightarrow -5x^2 = -20 \\
\Leftrightarrow x^2 = \frac{-20}{-5}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(3(-7x^2+7)=-(20x^2+175) \\ \Leftrightarrow -21x^2+21=-20x^2-175 \\
\Leftrightarrow -21x^2+20x^2=-175-21 \\
\Leftrightarrow -x^2 = -196 \\
\Leftrightarrow x^2 = \frac{-196}{-1}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(2x^2-8=0 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(3(2x^2-3)=-(-14x^2+81) \\ \Leftrightarrow 6x^2-9=14x^2-81 \\
\Leftrightarrow 6x^2-14x^2=-81+9 \\
\Leftrightarrow -8x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{-8}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(7x^2+15=8x^2+6 \\ \Leftrightarrow 7x^2-8x^2=6-15 \\
\Leftrightarrow -x^2 = -9 \\
\Leftrightarrow x^2 = \frac{-9}{-1}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-x^2-503=4x^2-3 \\ \Leftrightarrow -x^2-4x^2=-3+503 \\
\Leftrightarrow -5x^2 = 500 \\
\Leftrightarrow x^2 = \frac{500}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2-193=-3x^2+7 \\ \Leftrightarrow -5x^2+3x^2=7+193 \\
\Leftrightarrow -2x^2 = 200 \\
\Leftrightarrow x^2 = \frac{200}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)