Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-8x^2-1152=0\)
- \(8x^2-392=0\)
- \(-13x^2-8=-10x^2-8\)
- \(-2(6x^2-9)=-(9x^2+414)\)
- \(-13x^2-593=-10x^2-5\)
- \(-8x^2+668=-5x^2-7\)
- \(-6x^2-230=-7x^2-5\)
- \(18x^2-970=10x^2-2\)
- \(-4x^2+4=-9x^2+9\)
- \(-4(-6x^2+6)=-(-32x^2-1328)\)
- \(7x^2+7=0\)
- \(2(-10x^2-6)=-(24x^2-132)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-8x^2-1152=0 \\
\Leftrightarrow -8x^2 = 1152 \\
\Leftrightarrow x^2 = \frac{1152}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2-392=0 \\
\Leftrightarrow 8x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{8}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-13x^2-8=-10x^2-8 \\ \Leftrightarrow -13x^2+10x^2=-8+8 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2(6x^2-9)=-(9x^2+414) \\ \Leftrightarrow -12x^2+18=-9x^2-414 \\
\Leftrightarrow -12x^2+9x^2=-414-18 \\
\Leftrightarrow -3x^2 = -432 \\
\Leftrightarrow x^2 = \frac{-432}{-3}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-13x^2-593=-10x^2-5 \\ \Leftrightarrow -13x^2+10x^2=-5+593 \\
\Leftrightarrow -3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+668=-5x^2-7 \\ \Leftrightarrow -8x^2+5x^2=-7-668 \\
\Leftrightarrow -3x^2 = -675 \\
\Leftrightarrow x^2 = \frac{-675}{-3}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-6x^2-230=-7x^2-5 \\ \Leftrightarrow -6x^2+7x^2=-5+230 \\
\Leftrightarrow x^2 = 225 \\
\Leftrightarrow x^2 = \frac{225}{1}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(18x^2-970=10x^2-2 \\ \Leftrightarrow 18x^2-10x^2=-2+970 \\
\Leftrightarrow 8x^2 = 968 \\
\Leftrightarrow x^2 = \frac{968}{8}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4x^2+4=-9x^2+9 \\ \Leftrightarrow -4x^2+9x^2=9-4 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-4(-6x^2+6)=-(-32x^2-1328) \\ \Leftrightarrow 24x^2-24=32x^2+1328 \\
\Leftrightarrow 24x^2-32x^2=1328+24 \\
\Leftrightarrow -8x^2 = 1352 \\
\Leftrightarrow x^2 = \frac{1352}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2+7=0 \\
\Leftrightarrow 7x^2 = -7 \\
\Leftrightarrow x^2 = \frac{-7}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(-10x^2-6)=-(24x^2-132) \\ \Leftrightarrow -20x^2-12=-24x^2+132 \\
\Leftrightarrow -20x^2+24x^2=132+12 \\
\Leftrightarrow 4x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{4}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)