Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2-54=0\)
2. \(4(-6x^2+9)=-(28x^2-20)\)
3. \(14x^2+973=9x^2-7\)
4. \(14x^2-396=9x^2+9\)
5. \(-3(-5x^2-3)=-(-13x^2-7)\)
6. \(-4(-10x^2-4)=-(-43x^2-163)\)
7. \(-4(-8x^2+6)=-(-27x^2-1101)\)
8. \(-2x^2+297=4x^2+3\)
9. \(-3x^2+12=0\)
10. \(-3x^2+27=0\)
11. \(x^2+239=6x^2-6\)
12. \(-2(-2x^2+2)=-(-11x^2+32)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2-54=0 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(4(-6x^2+9)=-(28x^2-20) \\ \Leftrightarrow -24x^2+36=-28x^2+20 \\ \Leftrightarrow -24x^2+28x^2=20-36 \\ \Leftrightarrow 4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{4} < 0 \\ V = \varnothing \\ -----------------\)
3. \(14x^2+973=9x^2-7 \\ \Leftrightarrow 14x^2-9x^2=-7-973 \\ \Leftrightarrow 5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(14x^2-396=9x^2+9 \\ \Leftrightarrow 14x^2-9x^2=9+396 \\ \Leftrightarrow 5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(-3(-5x^2-3)=-(-13x^2-7) \\ \Leftrightarrow 15x^2+9=13x^2+7 \\ \Leftrightarrow 15x^2-13x^2=7-9 \\ \Leftrightarrow 2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(-10x^2-4)=-(-43x^2-163) \\ \Leftrightarrow 40x^2+16=43x^2+163 \\ \Leftrightarrow 40x^2-43x^2=163-16 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4(-8x^2+6)=-(-27x^2-1101) \\ \Leftrightarrow 32x^2-24=27x^2+1101 \\ \Leftrightarrow 32x^2-27x^2=1101+24 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-2x^2+297=4x^2+3 \\ \Leftrightarrow -2x^2-4x^2=3-297 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-3x^2+12=0 \\ \Leftrightarrow -3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{-3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-3x^2+27=0 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(x^2+239=6x^2-6 \\ \Leftrightarrow x^2-6x^2=-6-239 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(-2(-2x^2+2)=-(-11x^2+32) \\ \Leftrightarrow 4x^2-4=11x^2-32 \\ \Leftrightarrow 4x^2-11x^2=-32+4 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)