Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+484=0\)
2. \(-5(2x^2-8)=-(5x^2-40)\)
3. \(6x^2-33=9x^2-6\)
4. \(7x^2-973=2x^2+7\)
5. \(x^2-144=0\)
6. \(3(-9x^2-7)=-(19x^2+53)\)
7. \(4x^2+196=0\)
8. \(-11x^2-50=-8x^2-2\)
9. \(-3x^2-108=0\)
10. \(-3(-10x^2-2)=-(-36x^2+1344)\)
11. \(7x^2+0=0\)
12. \(8x^2+329=10x^2-9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+484=0 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-5(2x^2-8)=-(5x^2-40) \\ \Leftrightarrow -10x^2+40=-5x^2+40 \\ \Leftrightarrow -10x^2+5x^2=40-40 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(6x^2-33=9x^2-6 \\ \Leftrightarrow 6x^2-9x^2=-6+33 \\ \Leftrightarrow -3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(7x^2-973=2x^2+7 \\ \Leftrightarrow 7x^2-2x^2=7+973 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(x^2-144=0 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(3(-9x^2-7)=-(19x^2+53) \\ \Leftrightarrow -27x^2-21=-19x^2-53 \\ \Leftrightarrow -27x^2+19x^2=-53+21 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(4x^2+196=0 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-11x^2-50=-8x^2-2 \\ \Leftrightarrow -11x^2+8x^2=-2+50 \\ \Leftrightarrow -3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3x^2-108=0 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3(-10x^2-2)=-(-36x^2+1344) \\ \Leftrightarrow 30x^2+6=36x^2-1344 \\ \Leftrightarrow 30x^2-36x^2=-1344-6 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(8x^2+329=10x^2-9 \\ \Leftrightarrow 8x^2-10x^2=-9-329 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)