Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(x^2+702=8x^2+2\)
- \(x^2-144=0\)
- \(-6x^2+150=0\)
- \(6x^2+0=0\)
- \(2(10x^2+5)=-(-24x^2+90)\)
- \(10x^2-442=8x^2+8\)
- \(5(10x^2-9)=-(-54x^2+445)\)
- \(-10x^2-349=-3x^2-6\)
- \(-3x^2-9=-4x^2-9\)
- \(3x^2-840=8x^2+5\)
- \(6x^2-216=0\)
- \(5x^2-1125=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(x^2+702=8x^2+2 \\ \Leftrightarrow x^2-8x^2=2-702 \\
\Leftrightarrow -7x^2 = -700 \\
\Leftrightarrow x^2 = \frac{-700}{-7}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(x^2-144=0 \\
\Leftrightarrow x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{1}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-6x^2+150=0 \\
\Leftrightarrow -6x^2 = -150 \\
\Leftrightarrow x^2 = \frac{-150}{-6}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(6x^2+0=0 \\
\Leftrightarrow 6x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{6}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2(10x^2+5)=-(-24x^2+90) \\ \Leftrightarrow 20x^2+10=24x^2-90 \\
\Leftrightarrow 20x^2-24x^2=-90-10 \\
\Leftrightarrow -4x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-4}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(10x^2-442=8x^2+8 \\ \Leftrightarrow 10x^2-8x^2=8+442 \\
\Leftrightarrow 2x^2 = 450 \\
\Leftrightarrow x^2 = \frac{450}{2}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(5(10x^2-9)=-(-54x^2+445) \\ \Leftrightarrow 50x^2-45=54x^2-445 \\
\Leftrightarrow 50x^2-54x^2=-445+45 \\
\Leftrightarrow -4x^2 = -400 \\
\Leftrightarrow x^2 = \frac{-400}{-4}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-10x^2-349=-3x^2-6 \\ \Leftrightarrow -10x^2+3x^2=-6+349 \\
\Leftrightarrow -7x^2 = 343 \\
\Leftrightarrow x^2 = \frac{343}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2-9=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9+9 \\
\Leftrightarrow x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(3x^2-840=8x^2+5 \\ \Leftrightarrow 3x^2-8x^2=5+840 \\
\Leftrightarrow -5x^2 = 845 \\
\Leftrightarrow x^2 = \frac{845}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-216=0 \\
\Leftrightarrow 6x^2 = 216 \\
\Leftrightarrow x^2 = \frac{216}{6}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(5x^2-1125=0 \\
\Leftrightarrow 5x^2 = 1125 \\
\Leftrightarrow x^2 = \frac{1125}{5}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)