Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-10x^2+159=-8x^2-3\)
- \(-2(-6x^2-10)=-(-11x^2+29)\)
- \(-15x^2-68=-7x^2+4\)
- \(-7x^2-48=-2x^2-3\)
- \(-4x^2-676=0\)
- \(-3x^2+432=0\)
- \(7x^2-1008=0\)
- \(-5(-10x^2-4)=-(-53x^2-20)\)
- \(-15x^2+10=-9x^2+10\)
- \(x^2+0=0\)
- \(4x^2-144=0\)
- \(-2(8x^2-8)=-(11x^2+29)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-10x^2+159=-8x^2-3 \\ \Leftrightarrow -10x^2+8x^2=-3-159 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-2(-6x^2-10)=-(-11x^2+29) \\ \Leftrightarrow 12x^2+20=11x^2-29 \\
\Leftrightarrow 12x^2-11x^2=-29-20 \\
\Leftrightarrow x^2 = -49 \\
\Leftrightarrow x^2 = \frac{-49}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-15x^2-68=-7x^2+4 \\ \Leftrightarrow -15x^2+7x^2=4+68 \\
\Leftrightarrow -8x^2 = 72 \\
\Leftrightarrow x^2 = \frac{72}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-48=-2x^2-3 \\ \Leftrightarrow -7x^2+2x^2=-3+48 \\
\Leftrightarrow -5x^2 = 45 \\
\Leftrightarrow x^2 = \frac{45}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2-676=0 \\
\Leftrightarrow -4x^2 = 676 \\
\Leftrightarrow x^2 = \frac{676}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+432=0 \\
\Leftrightarrow -3x^2 = -432 \\
\Leftrightarrow x^2 = \frac{-432}{-3}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(7x^2-1008=0 \\
\Leftrightarrow 7x^2 = 1008 \\
\Leftrightarrow x^2 = \frac{1008}{7}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-5(-10x^2-4)=-(-53x^2-20) \\ \Leftrightarrow 50x^2+20=53x^2+20 \\
\Leftrightarrow 50x^2-53x^2=20-20 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-15x^2+10=-9x^2+10 \\ \Leftrightarrow -15x^2+9x^2=10-10 \\
\Leftrightarrow -6x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-6}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(x^2+0=0 \\
\Leftrightarrow x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(4x^2-144=0 \\
\Leftrightarrow 4x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{4}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-2(8x^2-8)=-(11x^2+29) \\ \Leftrightarrow -16x^2+16=-11x^2-29 \\
\Leftrightarrow -16x^2+11x^2=-29-16 \\
\Leftrightarrow -5x^2 = -45 \\
\Leftrightarrow x^2 = \frac{-45}{-5}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)