Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-8=0\)
2. \(5x^2-500=0\)
3. \(-5x^2+0=0\)
4. \(-x^2-2=-8x^2-2\)
5. \(-7x^2-112=0\)
6. \(-4(-10x^2+9)=-(-39x^2-85)\)
7. \(4(9x^2-7)=-(-34x^2-134)\)
8. \(-x^2+115=6x^2+3\)
9. \(6x^2+216=0\)
10. \(-4(3x^2-7)=-(19x^2-140)\)
11. \(-8x^2-288=0\)
12. \(8x^2+203=9x^2+7\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-8=0 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(5x^2-500=0 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-x^2-2=-8x^2-2 \\ \Leftrightarrow -x^2+8x^2=-2+2 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-7x^2-112=0 \\ \Leftrightarrow -7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{-7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(-10x^2+9)=-(-39x^2-85) \\ \Leftrightarrow 40x^2-36=39x^2+85 \\ \Leftrightarrow 40x^2-39x^2=85+36 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(4(9x^2-7)=-(-34x^2-134) \\ \Leftrightarrow 36x^2-28=34x^2+134 \\ \Leftrightarrow 36x^2-34x^2=134+28 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(-x^2+115=6x^2+3 \\ \Leftrightarrow -x^2-6x^2=3-115 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(6x^2+216=0 \\ \Leftrightarrow 6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4(3x^2-7)=-(19x^2-140) \\ \Leftrightarrow -12x^2+28=-19x^2+140 \\ \Leftrightarrow -12x^2+19x^2=140-28 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-8x^2-288=0 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(8x^2+203=9x^2+7 \\ \Leftrightarrow 8x^2-9x^2=7-203 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)