Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-153=-10x^2+9\)
2. \(-3x^2+75=0\)
3. \(-3(-4x^2-10)=-(-15x^2-177)\)
4. \(-2(-3x^2-3)=-(-x^2-326)\)
5. \(4(4x^2+5)=-(-17x^2+44)\)
6. \(-10x^2-34=-2x^2-2\)
7. \(4(7x^2+10)=-(-31x^2+107)\)
8. \(3x^2+147=0\)
9. \(6x^2-422=9x^2+10\)
10. \(-4(10x^2+2)=-(46x^2-718)\)
11. \(-8x^2-2=-3x^2-7\)
12. \(8x^2-1152=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-153=-10x^2+9 \\ \Leftrightarrow -8x^2+10x^2=9+153 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(-3x^2+75=0 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(-3(-4x^2-10)=-(-15x^2-177) \\ \Leftrightarrow 12x^2+30=15x^2+177 \\ \Leftrightarrow 12x^2-15x^2=177-30 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2(-3x^2-3)=-(-x^2-326) \\ \Leftrightarrow 6x^2+6=x^2+326 \\ \Leftrightarrow 6x^2-x^2=326-6 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(4(4x^2+5)=-(-17x^2+44) \\ \Leftrightarrow 16x^2+20=17x^2-44 \\ \Leftrightarrow 16x^2-17x^2=-44-20 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(-10x^2-34=-2x^2-2 \\ \Leftrightarrow -10x^2+2x^2=-2+34 \\ \Leftrightarrow -8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{-8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(4(7x^2+10)=-(-31x^2+107) \\ \Leftrightarrow 28x^2+40=31x^2-107 \\ \Leftrightarrow 28x^2-31x^2=-107-40 \\ \Leftrightarrow -3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{-3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(3x^2+147=0 \\ \Leftrightarrow 3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(6x^2-422=9x^2+10 \\ \Leftrightarrow 6x^2-9x^2=10+422 \\ \Leftrightarrow -3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4(10x^2+2)=-(46x^2-718) \\ \Leftrightarrow -40x^2-8=-46x^2+718 \\ \Leftrightarrow -40x^2+46x^2=718+8 \\ \Leftrightarrow 6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-8x^2-2=-3x^2-7 \\ \Leftrightarrow -8x^2+3x^2=-7+2 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(8x^2-1152=0 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)