Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(4x^2+2)=-(19x^2-1)\)
2. \(5(3x^2-4)=-(-9x^2-580)\)
3. \(-3(7x^2+10)=-(23x^2+480)\)
4. \(4x^2-670=8x^2+6\)
5. \(5x^2-80=0\)
6. \(6x^2-330=2x^2-6\)
7. \(-5x^2+80=0\)
8. \(6x^2-580=9x^2+8\)
9. \(-8x^2+7=-9x^2+7\)
10. \(5x^2+6=3x^2+6\)
11. \(4x^2-900=0\)
12. \(4x^2-117=3x^2+4\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(4x^2+2)=-(19x^2-1) \\ \Leftrightarrow -12x^2-6=-19x^2+1 \\ \Leftrightarrow -12x^2+19x^2=1+6 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(5(3x^2-4)=-(-9x^2-580) \\ \Leftrightarrow 15x^2-20=9x^2+580 \\ \Leftrightarrow 15x^2-9x^2=580+20 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-3(7x^2+10)=-(23x^2+480) \\ \Leftrightarrow -21x^2-30=-23x^2-480 \\ \Leftrightarrow -21x^2+23x^2=-480+30 \\ \Leftrightarrow 2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(4x^2-670=8x^2+6 \\ \Leftrightarrow 4x^2-8x^2=6+670 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(5x^2-80=0 \\ \Leftrightarrow 5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(6x^2-330=2x^2-6 \\ \Leftrightarrow 6x^2-2x^2=-6+330 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-5x^2+80=0 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(6x^2-580=9x^2+8 \\ \Leftrightarrow 6x^2-9x^2=8+580 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-8x^2+7=-9x^2+7 \\ \Leftrightarrow -8x^2+9x^2=7-7 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(5x^2+6=3x^2+6 \\ \Leftrightarrow 5x^2-3x^2=6-6 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(4x^2-900=0 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(4x^2-117=3x^2+4 \\ \Leftrightarrow 4x^2-3x^2=4+117 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)