Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+0=0\)
2. \(-5x^2+717=-10x^2-3\)
3. \(-4x^2-36=0\)
4. \(6x^2+384=0\)
5. \(4x^2-481=-2x^2+5\)
6. \(-4x^2+36=0\)
7. \(-7x^2-1183=0\)
8. \(-5x^2-80=0\)
9. \(-4x^2-503=-7x^2+4\)
10. \(7x^2+0=0\)
11. \(-6x^2+1176=0\)
12. \(3(9x^2-9)=-(-26x^2-94)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-5x^2+717=-10x^2-3 \\ \Leftrightarrow -5x^2+10x^2=-3-717 \\ \Leftrightarrow 5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-4x^2-36=0 \\ \Leftrightarrow -4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(6x^2+384=0 \\ \Leftrightarrow 6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{6} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4x^2-481=-2x^2+5 \\ \Leftrightarrow 4x^2+2x^2=5+481 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-4x^2+36=0 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(-7x^2-1183=0 \\ \Leftrightarrow -7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{-7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5x^2-80=0 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-4x^2-503=-7x^2+4 \\ \Leftrightarrow -4x^2+7x^2=4+503 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-6x^2+1176=0 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(3(9x^2-9)=-(-26x^2-94) \\ \Leftrightarrow 27x^2-27=26x^2+94 \\ \Leftrightarrow 27x^2-26x^2=94+27 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)