Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2(7x^2-5)=-(-17x^2-65)\)
- \(3(3x^2+8)=-(-11x^2+138)\)
- \(8x^2-968=0\)
- \(5x^2-52=3x^2-2\)
- \(-5x^2+320=0\)
- \(16x^2-260=9x^2-8\)
- \(3(-6x^2-3)=-(26x^2+9)\)
- \(-x^2-225=0\)
- \(-3x^2+0=0\)
- \(-5(10x^2-5)=-(48x^2-187)\)
- \(2x^2-8=0\)
- \(-13x^2+1148=-5x^2-4\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2(7x^2-5)=-(-17x^2-65) \\ \Leftrightarrow 14x^2-10=17x^2+65 \\
\Leftrightarrow 14x^2-17x^2=65+10 \\
\Leftrightarrow -3x^2 = 75 \\
\Leftrightarrow x^2 = \frac{75}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(3x^2+8)=-(-11x^2+138) \\ \Leftrightarrow 9x^2+24=11x^2-138 \\
\Leftrightarrow 9x^2-11x^2=-138-24 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(8x^2-968=0 \\
\Leftrightarrow 8x^2 = 968 \\
\Leftrightarrow x^2 = \frac{968}{8}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(5x^2-52=3x^2-2 \\ \Leftrightarrow 5x^2-3x^2=-2+52 \\
\Leftrightarrow 2x^2 = 50 \\
\Leftrightarrow x^2 = \frac{50}{2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-5x^2+320=0 \\
\Leftrightarrow -5x^2 = -320 \\
\Leftrightarrow x^2 = \frac{-320}{-5}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(16x^2-260=9x^2-8 \\ \Leftrightarrow 16x^2-9x^2=-8+260 \\
\Leftrightarrow 7x^2 = 252 \\
\Leftrightarrow x^2 = \frac{252}{7}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(3(-6x^2-3)=-(26x^2+9) \\ \Leftrightarrow -18x^2-9=-26x^2-9 \\
\Leftrightarrow -18x^2+26x^2=-9+9 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-x^2-225=0 \\
\Leftrightarrow -x^2 = 225 \\
\Leftrightarrow x^2 = \frac{225}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+0=0 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-5(10x^2-5)=-(48x^2-187) \\ \Leftrightarrow -50x^2+25=-48x^2+187 \\
\Leftrightarrow -50x^2+48x^2=187-25 \\
\Leftrightarrow -2x^2 = 162 \\
\Leftrightarrow x^2 = \frac{162}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2-8=0 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-13x^2+1148=-5x^2-4 \\ \Leftrightarrow -13x^2+5x^2=-4-1148 \\
\Leftrightarrow -8x^2 = -1152 \\
\Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)