Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(7x^2+5)=-(-29x^2-983)\)
2. \(5(6x^2-2)=-(-26x^2+74)\)
3. \(-2x^2+28=-3x^2+3\)
4. \(-11x^2+608=-5x^2+8\)
5. \(-5x^2-605=0\)
6. \(9x^2-93=5x^2+7\)
7. \(-3(-6x^2-8)=-(-21x^2+219)\)
8. \(-x^2-9=0\)
9. \(5(10x^2+6)=-(-46x^2+454)\)
10. \(-2(-10x^2+3)=-(-12x^2+654)\)
11. \(13x^2-7=8x^2-7\)
12. \(-2(-6x^2+6)=-(-7x^2-68)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(7x^2+5)=-(-29x^2-983) \\ \Leftrightarrow 21x^2+15=29x^2+983 \\ \Leftrightarrow 21x^2-29x^2=983-15 \\ \Leftrightarrow -8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(5(6x^2-2)=-(-26x^2+74) \\ \Leftrightarrow 30x^2-10=26x^2-74 \\ \Leftrightarrow 30x^2-26x^2=-74+10 \\ \Leftrightarrow 4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-2x^2+28=-3x^2+3 \\ \Leftrightarrow -2x^2+3x^2=3-28 \\ \Leftrightarrow x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-11x^2+608=-5x^2+8 \\ \Leftrightarrow -11x^2+5x^2=8-608 \\ \Leftrightarrow -6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{-6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-5x^2-605=0 \\ \Leftrightarrow -5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(9x^2-93=5x^2+7 \\ \Leftrightarrow 9x^2-5x^2=7+93 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-3(-6x^2-8)=-(-21x^2+219) \\ \Leftrightarrow 18x^2+24=21x^2-219 \\ \Leftrightarrow 18x^2-21x^2=-219-24 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(-x^2-9=0 \\ \Leftrightarrow -x^2 = 9 \\ \Leftrightarrow x^2 = \frac{9}{-1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5(10x^2+6)=-(-46x^2+454) \\ \Leftrightarrow 50x^2+30=46x^2-454 \\ \Leftrightarrow 50x^2-46x^2=-454-30 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(-10x^2+3)=-(-12x^2+654) \\ \Leftrightarrow 20x^2-6=12x^2-654 \\ \Leftrightarrow 20x^2-12x^2=-654+6 \\ \Leftrightarrow 8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(13x^2-7=8x^2-7 \\ \Leftrightarrow 13x^2-8x^2=-7+7 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-2(-6x^2+6)=-(-7x^2-68) \\ \Leftrightarrow 12x^2-12=7x^2+68 \\ \Leftrightarrow 12x^2-7x^2=68+12 \\ \Leftrightarrow 5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)