Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(11x^2-208=5x^2+8\)
2. \(-3(-4x^2+10)=-(-4x^2-258)\)
3. \(15x^2-10=9x^2-4\)
4. \(-8x^2-1800=0\)
5. \(2(-3x^2+2)=-(2x^2+0)\)
6. \(2x^2+288=0\)
7. \(-3x^2+48=0\)
8. \(8x^2-800=0\)
9. \(-6x^2-9=-10x^2-9\)
10. \(-5x^2+0=0\)
11. \(4x^2+256=0\)
12. \(2(-8x^2+5)=-(20x^2-910)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(11x^2-208=5x^2+8 \\ \Leftrightarrow 11x^2-5x^2=8+208 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-3(-4x^2+10)=-(-4x^2-258) \\ \Leftrightarrow 12x^2-30=4x^2+258 \\ \Leftrightarrow 12x^2-4x^2=258+30 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(15x^2-10=9x^2-4 \\ \Leftrightarrow 15x^2-9x^2=-4+10 \\ \Leftrightarrow 6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-8x^2-1800=0 \\ \Leftrightarrow -8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2(-3x^2+2)=-(2x^2+0) \\ \Leftrightarrow -6x^2+4=-2x^2+0 \\ \Leftrightarrow -6x^2+2x^2=0-4 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(2x^2+288=0 \\ \Leftrightarrow 2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-3x^2+48=0 \\ \Leftrightarrow -3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{-3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(8x^2-800=0 \\ \Leftrightarrow 8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-6x^2-9=-10x^2-9 \\ \Leftrightarrow -6x^2+10x^2=-9+9 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(4x^2+256=0 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(-8x^2+5)=-(20x^2-910) \\ \Leftrightarrow -16x^2+10=-20x^2+910 \\ \Leftrightarrow -16x^2+20x^2=910-10 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)