Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+26=8x^2-2\)
2. \(5(-7x^2+6)=-(27x^2+170)\)
3. \(5x^2+500=0\)
4. \(5x^2+125=0\)
5. \(2x^2-5=-5x^2-5\)
6. \(4x^2-784=0\)
7. \(5(-6x^2+4)=-(34x^2+236)\)
8. \(-4(10x^2+8)=-(41x^2+228)\)
9. \(-6x^2-216=0\)
10. \(3(-3x^2+2)=-(13x^2-70)\)
11. \(-2x^2+2=0\)
12. \(5x^2-405=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+26=8x^2-2 \\ \Leftrightarrow x^2-8x^2=-2-26 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(5(-7x^2+6)=-(27x^2+170) \\ \Leftrightarrow -35x^2+30=-27x^2-170 \\ \Leftrightarrow -35x^2+27x^2=-170-30 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(5x^2+500=0 \\ \Leftrightarrow 5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5x^2+125=0 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2x^2-5=-5x^2-5 \\ \Leftrightarrow 2x^2+5x^2=-5+5 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(4x^2-784=0 \\ \Leftrightarrow 4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(5(-6x^2+4)=-(34x^2+236) \\ \Leftrightarrow -30x^2+20=-34x^2-236 \\ \Leftrightarrow -30x^2+34x^2=-236-20 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-4(10x^2+8)=-(41x^2+228) \\ \Leftrightarrow -40x^2-32=-41x^2-228 \\ \Leftrightarrow -40x^2+41x^2=-228+32 \\ \Leftrightarrow x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-6x^2-216=0 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(3(-3x^2+2)=-(13x^2-70) \\ \Leftrightarrow -9x^2+6=-13x^2+70 \\ \Leftrightarrow -9x^2+13x^2=70-6 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-2x^2+2=0 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(5x^2-405=0 \\ \Leftrightarrow 5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)