Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2-6=0\)
2. \(-5x^2+474=-9x^2-10\)
3. \(6x^2-1350=0\)
4. \(5(4x^2-5)=-(-27x^2+1033)\)
5. \(-4(-9x^2-8)=-(-43x^2+31)\)
6. \(3x^2+0=0\)
7. \(-5x^2+0=0\)
8. \(2(-10x^2-9)=-(17x^2-282)\)
9. \(-11x^2-92=-10x^2+8\)
10. \(8x^2-41=6x^2-9\)
11. \(4(9x^2-8)=-(-30x^2+86)\)
12. \(2(-3x^2-5)=-(0x^2+1024)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2-6=0 \\ \Leftrightarrow -6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{-6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-5x^2+474=-9x^2-10 \\ \Leftrightarrow -5x^2+9x^2=-10-474 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(6x^2-1350=0 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(5(4x^2-5)=-(-27x^2+1033) \\ \Leftrightarrow 20x^2-25=27x^2-1033 \\ \Leftrightarrow 20x^2-27x^2=-1033+25 \\ \Leftrightarrow -7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{-7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-4(-9x^2-8)=-(-43x^2+31) \\ \Leftrightarrow 36x^2+32=43x^2-31 \\ \Leftrightarrow 36x^2-43x^2=-31-32 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(2(-10x^2-9)=-(17x^2-282) \\ \Leftrightarrow -20x^2-18=-17x^2+282 \\ \Leftrightarrow -20x^2+17x^2=282+18 \\ \Leftrightarrow -3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-11x^2-92=-10x^2+8 \\ \Leftrightarrow -11x^2+10x^2=8+92 \\ \Leftrightarrow -x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(8x^2-41=6x^2-9 \\ \Leftrightarrow 8x^2-6x^2=-9+41 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(4(9x^2-8)=-(-30x^2+86) \\ \Leftrightarrow 36x^2-32=30x^2-86 \\ \Leftrightarrow 36x^2-30x^2=-86+32 \\ \Leftrightarrow 6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(-3x^2-5)=-(0x^2+1024) \\ \Leftrightarrow -6x^2-10=0x^2-1024 \\ \Leftrightarrow -6x^2+0x^2=-1024+10 \\ \Leftrightarrow -6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)