Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-459=-3x^2-9\)
2. \(-4x^2+676=0\)
3. \(5x^2+173=6x^2+4\)
4. \(6x^2-1350=0\)
5. \(-7x^2-112=0\)
6. \(-4(-3x^2-6)=-(-8x^2-600)\)
7. \(-4(-2x^2-5)=-(-4x^2-696)\)
8. \(4x^2+6=9x^2+6\)
9. \(-4x^2+324=0\)
10. \(-5(-9x^2+3)=-(-41x^2+211)\)
11. \(-x^2-41=-9x^2-9\)
12. \(-x^2-130=-3x^2-2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-459=-3x^2-9 \\ \Leftrightarrow -x^2+3x^2=-9+459 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-4x^2+676=0 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(5x^2+173=6x^2+4 \\ \Leftrightarrow 5x^2-6x^2=4-173 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(6x^2-1350=0 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-7x^2-112=0 \\ \Leftrightarrow -7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{-7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(-3x^2-6)=-(-8x^2-600) \\ \Leftrightarrow 12x^2+24=8x^2+600 \\ \Leftrightarrow 12x^2-8x^2=600-24 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(-4(-2x^2-5)=-(-4x^2-696) \\ \Leftrightarrow 8x^2+20=4x^2+696 \\ \Leftrightarrow 8x^2-4x^2=696-20 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(4x^2+6=9x^2+6 \\ \Leftrightarrow 4x^2-9x^2=6-6 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-4x^2+324=0 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-5(-9x^2+3)=-(-41x^2+211) \\ \Leftrightarrow 45x^2-15=41x^2-211 \\ \Leftrightarrow 45x^2-41x^2=-211+15 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-x^2-41=-9x^2-9 \\ \Leftrightarrow -x^2+9x^2=-9+41 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-x^2-130=-3x^2-2 \\ \Leftrightarrow -x^2+3x^2=-2+130 \\ \Leftrightarrow 2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)