Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(5(8x^2-7)=-(-43x^2+35)\)
- \(-x^2-1004=-7x^2+10\)
- \(-10x^2+206=-6x^2+10\)
- \(-2(-10x^2+3)=-(-19x^2+7)\)
- \(2(-9x^2-4)=-(25x^2-692)\)
- \(-2(-10x^2+9)=-(-16x^2+18)\)
- \(-3x^2+108=0\)
- \(-4(-2x^2-8)=-(-3x^2-32)\)
- \(7x^2+196=10x^2+4\)
- \(13x^2+14=9x^2-2\)
- \(8x^2-1800=0\)
- \(6x^2-600=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(5(8x^2-7)=-(-43x^2+35) \\ \Leftrightarrow 40x^2-35=43x^2-35 \\
\Leftrightarrow 40x^2-43x^2=-35+35 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-x^2-1004=-7x^2+10 \\ \Leftrightarrow -x^2+7x^2=10+1004 \\
\Leftrightarrow 6x^2 = 1014 \\
\Leftrightarrow x^2 = \frac{1014}{6}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-10x^2+206=-6x^2+10 \\ \Leftrightarrow -10x^2+6x^2=10-206 \\
\Leftrightarrow -4x^2 = -196 \\
\Leftrightarrow x^2 = \frac{-196}{-4}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-2(-10x^2+3)=-(-19x^2+7) \\ \Leftrightarrow 20x^2-6=19x^2-7 \\
\Leftrightarrow 20x^2-19x^2=-7+6 \\
\Leftrightarrow x^2 = -1 \\
\Leftrightarrow x^2 = \frac{-1}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(-9x^2-4)=-(25x^2-692) \\ \Leftrightarrow -18x^2-8=-25x^2+692 \\
\Leftrightarrow -18x^2+25x^2=692+8 \\
\Leftrightarrow 7x^2 = 700 \\
\Leftrightarrow x^2 = \frac{700}{7}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-2(-10x^2+9)=-(-16x^2+18) \\ \Leftrightarrow 20x^2-18=16x^2-18 \\
\Leftrightarrow 20x^2-16x^2=-18+18 \\
\Leftrightarrow 4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3x^2+108=0 \\
\Leftrightarrow -3x^2 = -108 \\
\Leftrightarrow x^2 = \frac{-108}{-3}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(-4(-2x^2-8)=-(-3x^2-32) \\ \Leftrightarrow 8x^2+32=3x^2+32 \\
\Leftrightarrow 8x^2-3x^2=32-32 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(7x^2+196=10x^2+4 \\ \Leftrightarrow 7x^2-10x^2=4-196 \\
\Leftrightarrow -3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{-3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(13x^2+14=9x^2-2 \\ \Leftrightarrow 13x^2-9x^2=-2-14 \\
\Leftrightarrow 4x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2-1800=0 \\
\Leftrightarrow 8x^2 = 1800 \\
\Leftrightarrow x^2 = \frac{1800}{8}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(6x^2-600=0 \\
\Leftrightarrow 6x^2 = 600 \\
\Leftrightarrow x^2 = \frac{600}{6}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)