Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-512=0\)
2. \(6x^2-54=0\)
3. \(-7x^2-4=-3x^2-4\)
4. \(-11x^2+194=-8x^2+2\)
5. \(-3x^2+10=5x^2+2\)
6. \(-5(-8x^2+9)=-(-41x^2-55)\)
7. \(x^2-100=0\)
8. \(5x^2+0=0\)
9. \(-2x^2+247=-6x^2-9\)
10. \(-3x^2-507=0\)
11. \(-5x^2-6=-4x^2-6\)
12. \(-5x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-512=0 \\ \Leftrightarrow -8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(6x^2-54=0 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(-7x^2-4=-3x^2-4 \\ \Leftrightarrow -7x^2+3x^2=-4+4 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-11x^2+194=-8x^2+2 \\ \Leftrightarrow -11x^2+8x^2=2-194 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-3x^2+10=5x^2+2 \\ \Leftrightarrow -3x^2-5x^2=2-10 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-5(-8x^2+9)=-(-41x^2-55) \\ \Leftrightarrow 40x^2-45=41x^2+55 \\ \Leftrightarrow 40x^2-41x^2=55+45 \\ \Leftrightarrow -x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2-100=0 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(5x^2+0=0 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-2x^2+247=-6x^2-9 \\ \Leftrightarrow -2x^2+6x^2=-9-247 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3x^2-507=0 \\ \Leftrightarrow -3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{-3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5x^2-6=-4x^2-6 \\ \Leftrightarrow -5x^2+4x^2=-6+6 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)