Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(x^2-7=4x^2-4\)
- \(-8x^2+1152=0\)
- \(2(-4x^2-7)=-(2x^2+68)\)
- \(2x^2-50=0\)
- \(-5x^2-44=-8x^2+4\)
- \(-5(3x^2+4)=-(9x^2+1370)\)
- \(-8x^2+0=0\)
- \(2(-4x^2+9)=-(15x^2-81)\)
- \(9x^2+186=5x^2-10\)
- \(-7x^2+127=-2x^2+2\)
- \(3(5x^2-4)=-(-16x^2-52)\)
- \(8x^2+0=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(x^2-7=4x^2-4 \\ \Leftrightarrow x^2-4x^2=-4+7 \\
\Leftrightarrow -3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+1152=0 \\
\Leftrightarrow -8x^2 = -1152 \\
\Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(2(-4x^2-7)=-(2x^2+68) \\ \Leftrightarrow -8x^2-14=-2x^2-68 \\
\Leftrightarrow -8x^2+2x^2=-68+14 \\
\Leftrightarrow -6x^2 = -54 \\
\Leftrightarrow x^2 = \frac{-54}{-6}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(2x^2-50=0 \\
\Leftrightarrow 2x^2 = 50 \\
\Leftrightarrow x^2 = \frac{50}{2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-5x^2-44=-8x^2+4 \\ \Leftrightarrow -5x^2+8x^2=4+44 \\
\Leftrightarrow 3x^2 = 48 \\
\Leftrightarrow x^2 = \frac{48}{3}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-5(3x^2+4)=-(9x^2+1370) \\ \Leftrightarrow -15x^2-20=-9x^2-1370 \\
\Leftrightarrow -15x^2+9x^2=-1370+20 \\
\Leftrightarrow -6x^2 = -1350 \\
\Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2(-4x^2+9)=-(15x^2-81) \\ \Leftrightarrow -8x^2+18=-15x^2+81 \\
\Leftrightarrow -8x^2+15x^2=81-18 \\
\Leftrightarrow 7x^2 = 63 \\
\Leftrightarrow x^2 = \frac{63}{7}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(9x^2+186=5x^2-10 \\ \Leftrightarrow 9x^2-5x^2=-10-186 \\
\Leftrightarrow 4x^2 = -196 \\
\Leftrightarrow x^2 = \frac{-196}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2+127=-2x^2+2 \\ \Leftrightarrow -7x^2+2x^2=2-127 \\
\Leftrightarrow -5x^2 = -125 \\
\Leftrightarrow x^2 = \frac{-125}{-5}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(3(5x^2-4)=-(-16x^2-52) \\ \Leftrightarrow 15x^2-12=16x^2+52 \\
\Leftrightarrow 15x^2-16x^2=52+12 \\
\Leftrightarrow -x^2 = 64 \\
\Leftrightarrow x^2 = \frac{64}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2+0=0 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)