Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2x^2-18=0\)
- \(3(9x^2+3)=-(-31x^2+475)\)
- \(4x^2+900=0\)
- \(2(-7x^2+4)=-(18x^2+568)\)
- \(4(-2x^2+10)=-(7x^2-40)\)
- \(6x^2-96=0\)
- \(-8x^2+0=0\)
- \(2(-7x^2-7)=-(17x^2-13)\)
- \(7x^2-1372=0\)
- \(-5(4x^2+3)=-(14x^2+111)\)
- \(7x^2+678=10x^2+3\)
- \(-10x^2-5=-9x^2-9\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2x^2-18=0 \\
\Leftrightarrow -2x^2 = 18 \\
\Leftrightarrow x^2 = \frac{18}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(9x^2+3)=-(-31x^2+475) \\ \Leftrightarrow 27x^2+9=31x^2-475 \\
\Leftrightarrow 27x^2-31x^2=-475-9 \\
\Leftrightarrow -4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{-4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(4x^2+900=0 \\
\Leftrightarrow 4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(-7x^2+4)=-(18x^2+568) \\ \Leftrightarrow -14x^2+8=-18x^2-568 \\
\Leftrightarrow -14x^2+18x^2=-568-8 \\
\Leftrightarrow 4x^2 = -576 \\
\Leftrightarrow x^2 = \frac{-576}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(-2x^2+10)=-(7x^2-40) \\ \Leftrightarrow -8x^2+40=-7x^2+40 \\
\Leftrightarrow -8x^2+7x^2=40-40 \\
\Leftrightarrow -x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(6x^2-96=0 \\
\Leftrightarrow 6x^2 = 96 \\
\Leftrightarrow x^2 = \frac{96}{6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2(-7x^2-7)=-(17x^2-13) \\ \Leftrightarrow -14x^2-14=-17x^2+13 \\
\Leftrightarrow -14x^2+17x^2=13+14 \\
\Leftrightarrow 3x^2 = 27 \\
\Leftrightarrow x^2 = \frac{27}{3}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(7x^2-1372=0 \\
\Leftrightarrow 7x^2 = 1372 \\
\Leftrightarrow x^2 = \frac{1372}{7}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-5(4x^2+3)=-(14x^2+111) \\ \Leftrightarrow -20x^2-15=-14x^2-111 \\
\Leftrightarrow -20x^2+14x^2=-111+15 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(7x^2+678=10x^2+3 \\ \Leftrightarrow 7x^2-10x^2=3-678 \\
\Leftrightarrow -3x^2 = -675 \\
\Leftrightarrow x^2 = \frac{-675}{-3}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-10x^2-5=-9x^2-9 \\ \Leftrightarrow -10x^2+9x^2=-9+5 \\
\Leftrightarrow -x^2 = -4 \\
\Leftrightarrow x^2 = \frac{-4}{-1}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)