Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-7=4x^2-4\)
2. \(-8x^2+1152=0\)
3. \(2(-4x^2-7)=-(2x^2+68)\)
4. \(2x^2-50=0\)
5. \(-5x^2-44=-8x^2+4\)
6. \(-5(3x^2+4)=-(9x^2+1370)\)
7. \(-8x^2+0=0\)
8. \(2(-4x^2+9)=-(15x^2-81)\)
9. \(9x^2+186=5x^2-10\)
10. \(-7x^2+127=-2x^2+2\)
11. \(3(5x^2-4)=-(-16x^2-52)\)
12. \(8x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-7=4x^2-4 \\ \Leftrightarrow x^2-4x^2=-4+7 \\ \Leftrightarrow -3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{-3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-8x^2+1152=0 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(2(-4x^2-7)=-(2x^2+68) \\ \Leftrightarrow -8x^2-14=-2x^2-68 \\ \Leftrightarrow -8x^2+2x^2=-68+14 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(2x^2-50=0 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-5x^2-44=-8x^2+4 \\ \Leftrightarrow -5x^2+8x^2=4+44 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(-5(3x^2+4)=-(9x^2+1370) \\ \Leftrightarrow -15x^2-20=-9x^2-1370 \\ \Leftrightarrow -15x^2+9x^2=-1370+20 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(2(-4x^2+9)=-(15x^2-81) \\ \Leftrightarrow -8x^2+18=-15x^2+81 \\ \Leftrightarrow -8x^2+15x^2=81-18 \\ \Leftrightarrow 7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(9x^2+186=5x^2-10 \\ \Leftrightarrow 9x^2-5x^2=-10-186 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-7x^2+127=-2x^2+2 \\ \Leftrightarrow -7x^2+2x^2=2-127 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
11. \(3(5x^2-4)=-(-16x^2-52) \\ \Leftrightarrow 15x^2-12=16x^2+52 \\ \Leftrightarrow 15x^2-16x^2=52+12 \\ \Leftrightarrow -x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{-1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)