Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-98=-4x^2+10\)
2. \(-6x^2-4=-10x^2-4\)
3. \(-x^2+9=0\)
4. \(-3(-9x^2+10)=-(-23x^2-226)\)
5. \(4(5x^2+6)=-(-27x^2+984)\)
6. \(4(2x^2+8)=-(-12x^2+452)\)
7. \(6x^2-24=0\)
8. \(-6x^2+0=0\)
9. \(7x^2-175=0\)
10. \(-x^2-1188=-8x^2-5\)
11. \(6x^2+600=0\)
12. \(7x^2+1183=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-98=-4x^2+10 \\ \Leftrightarrow -x^2+4x^2=10+98 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-6x^2-4=-10x^2-4 \\ \Leftrightarrow -6x^2+10x^2=-4+4 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-x^2+9=0 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(-3(-9x^2+10)=-(-23x^2-226) \\ \Leftrightarrow 27x^2-30=23x^2+226 \\ \Leftrightarrow 27x^2-23x^2=226+30 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(4(5x^2+6)=-(-27x^2+984) \\ \Leftrightarrow 20x^2+24=27x^2-984 \\ \Leftrightarrow 20x^2-27x^2=-984-24 \\ \Leftrightarrow -7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{-7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(4(2x^2+8)=-(-12x^2+452) \\ \Leftrightarrow 8x^2+32=12x^2-452 \\ \Leftrightarrow 8x^2-12x^2=-452-32 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(6x^2-24=0 \\ \Leftrightarrow 6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(7x^2-175=0 \\ \Leftrightarrow 7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-x^2-1188=-8x^2-5 \\ \Leftrightarrow -x^2+8x^2=-5+1188 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(6x^2+600=0 \\ \Leftrightarrow 6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(7x^2+1183=0 \\ \Leftrightarrow 7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\ V = \varnothing \\ -----------------\)