Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-4x^2+372=-7x^2+9\)
- \(-4x^2-611=-9x^2-6\)
- \(-6x^2+384=0\)
- \(-2(-5x^2-3)=-(-13x^2+582)\)
- \(-2(-5x^2+7)=-(-11x^2+63)\)
- \(-8x^2-35=-10x^2-3\)
- \(-6x^2+54=0\)
- \(-13x^2+1576=-5x^2+8\)
- \(4(10x^2+2)=-(-47x^2+839)\)
- \(6x^2+24=0\)
- \(5x^2-180=0\)
- \(-3x^2+432=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-4x^2+372=-7x^2+9 \\ \Leftrightarrow -4x^2+7x^2=9-372 \\
\Leftrightarrow 3x^2 = -363 \\
\Leftrightarrow x^2 = \frac{-363}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2-611=-9x^2-6 \\ \Leftrightarrow -4x^2+9x^2=-6+611 \\
\Leftrightarrow 5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-6x^2+384=0 \\
\Leftrightarrow -6x^2 = -384 \\
\Leftrightarrow x^2 = \frac{-384}{-6}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-2(-5x^2-3)=-(-13x^2+582) \\ \Leftrightarrow 10x^2+6=13x^2-582 \\
\Leftrightarrow 10x^2-13x^2=-582-6 \\
\Leftrightarrow -3x^2 = -588 \\
\Leftrightarrow x^2 = \frac{-588}{-3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-2(-5x^2+7)=-(-11x^2+63) \\ \Leftrightarrow 10x^2-14=11x^2-63 \\
\Leftrightarrow 10x^2-11x^2=-63+14 \\
\Leftrightarrow -x^2 = -49 \\
\Leftrightarrow x^2 = \frac{-49}{-1}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-8x^2-35=-10x^2-3 \\ \Leftrightarrow -8x^2+10x^2=-3+35 \\
\Leftrightarrow 2x^2 = 32 \\
\Leftrightarrow x^2 = \frac{32}{2}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-6x^2+54=0 \\
\Leftrightarrow -6x^2 = -54 \\
\Leftrightarrow x^2 = \frac{-54}{-6}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-13x^2+1576=-5x^2+8 \\ \Leftrightarrow -13x^2+5x^2=8-1576 \\
\Leftrightarrow -8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(4(10x^2+2)=-(-47x^2+839) \\ \Leftrightarrow 40x^2+8=47x^2-839 \\
\Leftrightarrow 40x^2-47x^2=-839-8 \\
\Leftrightarrow -7x^2 = -847 \\
\Leftrightarrow x^2 = \frac{-847}{-7}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(6x^2+24=0 \\
\Leftrightarrow 6x^2 = -24 \\
\Leftrightarrow x^2 = \frac{-24}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2-180=0 \\
\Leftrightarrow 5x^2 = 180 \\
\Leftrightarrow x^2 = \frac{180}{5}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-3x^2+432=0 \\
\Leftrightarrow -3x^2 = -432 \\
\Leftrightarrow x^2 = \frac{-432}{-3}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)