Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-11x^2+236=-6x^2-9\)
2. \(11x^2+230=10x^2+5\)
3. \(3(-10x^2-7)=-(31x^2+5)\)
4. \(-5(5x^2-6)=-(22x^2+645)\)
5. \(-7x^2+567=0\)
6. \(-2(-8x^2-5)=-(-17x^2-9)\)
7. \(-6x^2+384=0\)
8. \(5x^2+168=3x^2+6\)
9. \(5(9x^2+4)=-(-37x^2-220)\)
10. \(5x^2-80=0\)
11. \(-5x^2-2=-6x^2-2\)
12. \(-8x^2+200=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-11x^2+236=-6x^2-9 \\ \Leftrightarrow -11x^2+6x^2=-9-236 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(11x^2+230=10x^2+5 \\ \Leftrightarrow 11x^2-10x^2=5-230 \\ \Leftrightarrow x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3(-10x^2-7)=-(31x^2+5) \\ \Leftrightarrow -30x^2-21=-31x^2-5 \\ \Leftrightarrow -30x^2+31x^2=-5+21 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-5(5x^2-6)=-(22x^2+645) \\ \Leftrightarrow -25x^2+30=-22x^2-645 \\ \Leftrightarrow -25x^2+22x^2=-645-30 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-7x^2+567=0 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-2(-8x^2-5)=-(-17x^2-9) \\ \Leftrightarrow 16x^2+10=17x^2+9 \\ \Leftrightarrow 16x^2-17x^2=9-10 \\ \Leftrightarrow -x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{-1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-6x^2+384=0 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(5x^2+168=3x^2+6 \\ \Leftrightarrow 5x^2-3x^2=6-168 \\ \Leftrightarrow 2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5(9x^2+4)=-(-37x^2-220) \\ \Leftrightarrow 45x^2+20=37x^2+220 \\ \Leftrightarrow 45x^2-37x^2=220-20 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(5x^2-80=0 \\ \Leftrightarrow 5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-5x^2-2=-6x^2-2 \\ \Leftrightarrow -5x^2+6x^2=-2+2 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-8x^2+200=0 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)