Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-2x^2+7)=-(-4x^2+35)\)
2. \(-5x^2+500=0\)
3. \(12x^2-22=10x^2+10\)
4. \(-4(8x^2+6)=-(38x^2+750)\)
5. \(-5x^2-1=-7x^2-3\)
6. \(11x^2-110=4x^2+2\)
7. \(7x^2+191=3x^2-5\)
8. \(x^2+9=0\)
9. \(3(9x^2+6)=-(-25x^2-356)\)
10. \(-3(-7x^2+10)=-(-24x^2+393)\)
11. \(5(-4x^2-3)=-(13x^2+8)\)
12. \(-3x^2+216=-4x^2-9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-2x^2+7)=-(-4x^2+35) \\ \Leftrightarrow 10x^2-35=4x^2-35 \\ \Leftrightarrow 10x^2-4x^2=-35+35 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
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. \(12x^2-22=10x^2+10 \\ \Leftrightarrow 12x^2-10x^2=10+22 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-4(8x^2+6)=-(38x^2+750) \\ \Leftrightarrow -32x^2-24=-38x^2-750 \\ \Leftrightarrow -32x^2+38x^2=-750+24 \\ \Leftrightarrow 6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{6} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-5x^2-1=-7x^2-3 \\ \Leftrightarrow -5x^2+7x^2=-3+1 \\ \Leftrightarrow 2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(11x^2-110=4x^2+2 \\ \Leftrightarrow 11x^2-4x^2=2+110 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(7x^2+191=3x^2-5 \\ \Leftrightarrow 7x^2-3x^2=-5-191 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(x^2+9=0 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(9x^2+6)=-(-25x^2-356) \\ \Leftrightarrow 27x^2+18=25x^2+356 \\ \Leftrightarrow 27x^2-25x^2=356-18 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-3(-7x^2+10)=-(-24x^2+393) \\ \Leftrightarrow 21x^2-30=24x^2-393 \\ \Leftrightarrow 21x^2-24x^2=-393+30 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(5(-4x^2-3)=-(13x^2+8) \\ \Leftrightarrow -20x^2-15=-13x^2-8 \\ \Leftrightarrow -20x^2+13x^2=-8+15 \\ \Leftrightarrow -7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{-7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3x^2+216=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9-216 \\ \Leftrightarrow x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{1} < 0 \\ V = \varnothing \\ -----------------\)