Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3x^2+1790=5x^2-10\)
- \(3x^2-3=0\)
- \(3(-7x^2+2)=-(27x^2+858)\)
- \(-3(10x^2+4)=-(29x^2+13)\)
- \(-2(7x^2-2)=-(16x^2-292)\)
- \(2(-9x^2+7)=-(25x^2-14)\)
- \(-7x^2+1183=0\)
- \(5(7x^2-8)=-(-41x^2+1054)\)
- \(-3x^2+0=0\)
- \(5x^2-77=-3x^2-5\)
- \(-2x^2+72=0\)
- \(13x^2-670=10x^2+5\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3x^2+1790=5x^2-10 \\ \Leftrightarrow -3x^2-5x^2=-10-1790 \\
\Leftrightarrow -8x^2 = -1800 \\
\Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(3x^2-3=0 \\
\Leftrightarrow 3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(3(-7x^2+2)=-(27x^2+858) \\ \Leftrightarrow -21x^2+6=-27x^2-858 \\
\Leftrightarrow -21x^2+27x^2=-858-6 \\
\Leftrightarrow 6x^2 = -864 \\
\Leftrightarrow x^2 = \frac{-864}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(10x^2+4)=-(29x^2+13) \\ \Leftrightarrow -30x^2-12=-29x^2-13 \\
\Leftrightarrow -30x^2+29x^2=-13+12 \\
\Leftrightarrow -x^2 = -1 \\
\Leftrightarrow x^2 = \frac{-1}{-1}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-2(7x^2-2)=-(16x^2-292) \\ \Leftrightarrow -14x^2+4=-16x^2+292 \\
\Leftrightarrow -14x^2+16x^2=292-4 \\
\Leftrightarrow 2x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{2}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(2(-9x^2+7)=-(25x^2-14) \\ \Leftrightarrow -18x^2+14=-25x^2+14 \\
\Leftrightarrow -18x^2+25x^2=14-14 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-7x^2+1183=0 \\
\Leftrightarrow -7x^2 = -1183 \\
\Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(5(7x^2-8)=-(-41x^2+1054) \\ \Leftrightarrow 35x^2-40=41x^2-1054 \\
\Leftrightarrow 35x^2-41x^2=-1054+40 \\
\Leftrightarrow -6x^2 = -1014 \\
\Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-3x^2+0=0 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5x^2-77=-3x^2-5 \\ \Leftrightarrow 5x^2+3x^2=-5+77 \\
\Leftrightarrow 8x^2 = 72 \\
\Leftrightarrow x^2 = \frac{72}{8}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-2x^2+72=0 \\
\Leftrightarrow -2x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{-2}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(13x^2-670=10x^2+5 \\ \Leftrightarrow 13x^2-10x^2=5+670 \\
\Leftrightarrow 3x^2 = 675 \\
\Leftrightarrow x^2 = \frac{675}{3}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)