Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(7x^2-5)=-(-17x^2-65)\)
2. \(3(3x^2+8)=-(-11x^2+138)\)
3. \(8x^2-968=0\)
4. \(5x^2-52=3x^2-2\)
5. \(-5x^2+320=0\)
6. \(16x^2-260=9x^2-8\)
7. \(3(-6x^2-3)=-(26x^2+9)\)
8. \(-x^2-225=0\)
9. \(-3x^2+0=0\)
10. \(-5(10x^2-5)=-(48x^2-187)\)
11. \(2x^2-8=0\)
12. \(-13x^2+1148=-5x^2-4\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(7x^2-5)=-(-17x^2-65) \\ \Leftrightarrow 14x^2-10=17x^2+65 \\ \Leftrightarrow 14x^2-17x^2=65+10 \\ \Leftrightarrow -3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{-3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3(3x^2+8)=-(-11x^2+138) \\ \Leftrightarrow 9x^2+24=11x^2-138 \\ \Leftrightarrow 9x^2-11x^2=-138-24 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(8x^2-968=0 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(5x^2-52=3x^2-2 \\ \Leftrightarrow 5x^2-3x^2=-2+52 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-5x^2+320=0 \\ \Leftrightarrow -5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{-5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(16x^2-260=9x^2-8 \\ \Leftrightarrow 16x^2-9x^2=-8+260 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(3(-6x^2-3)=-(26x^2+9) \\ \Leftrightarrow -18x^2-9=-26x^2-9 \\ \Leftrightarrow -18x^2+26x^2=-9+9 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-x^2-225=0 \\ \Leftrightarrow -x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{-1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3x^2+0=0 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-5(10x^2-5)=-(48x^2-187) \\ \Leftrightarrow -50x^2+25=-48x^2+187 \\ \Leftrightarrow -50x^2+48x^2=187-25 \\ \Leftrightarrow -2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{-2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2-8=0 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-13x^2+1148=-5x^2-4 \\ \Leftrightarrow -13x^2+5x^2=-4-1148 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)