Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2+0=0\)
2. \(-2x^2+128=0\)
3. \(-4x^2-15=-10x^2-9\)
4. \(-5(5x^2-8)=-(29x^2-44)\)
5. \(2x^2-32=0\)
6. \(12x^2-248=7x^2-3\)
7. \(-3(10x^2-8)=-(32x^2-416)\)
8. \(-5(-6x^2-7)=-(-23x^2+973)\)
9. \(11x^2+602=5x^2+2\)
10. \(-4(-3x^2+9)=-(-17x^2+161)\)
11. \(2x^2-242=0\)
12. \(-3(-7x^2-9)=-(-18x^2-39)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2x^2+128=0 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(-4x^2-15=-10x^2-9 \\ \Leftrightarrow -4x^2+10x^2=-9+15 \\ \Leftrightarrow 6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-5(5x^2-8)=-(29x^2-44) \\ \Leftrightarrow -25x^2+40=-29x^2+44 \\ \Leftrightarrow -25x^2+29x^2=44-40 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(2x^2-32=0 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(12x^2-248=7x^2-3 \\ \Leftrightarrow 12x^2-7x^2=-3+248 \\ \Leftrightarrow 5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-3(10x^2-8)=-(32x^2-416) \\ \Leftrightarrow -30x^2+24=-32x^2+416 \\ \Leftrightarrow -30x^2+32x^2=416-24 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(-5(-6x^2-7)=-(-23x^2+973) \\ \Leftrightarrow 30x^2+35=23x^2-973 \\ \Leftrightarrow 30x^2-23x^2=-973-35 \\ \Leftrightarrow 7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(11x^2+602=5x^2+2 \\ \Leftrightarrow 11x^2-5x^2=2-602 \\ \Leftrightarrow 6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4(-3x^2+9)=-(-17x^2+161) \\ \Leftrightarrow 12x^2-36=17x^2-161 \\ \Leftrightarrow 12x^2-17x^2=-161+36 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
11. \(2x^2-242=0 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(-3(-7x^2-9)=-(-18x^2-39) \\ \Leftrightarrow 21x^2+27=18x^2+39 \\ \Leftrightarrow 21x^2-18x^2=39-27 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)