Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+200=0\)
2. \(-2x^2-7=-7x^2-2\)
3. \(3(-7x^2+6)=-(24x^2-30)\)
4. \(-17x^2+1573=-9x^2+5\)
5. \(-5(-3x^2+2)=-(-22x^2+577)\)
6. \(3x^2-363=0\)
7. \(-11x^2-73=-7x^2-9\)
8. \(-5(-3x^2+2)=-(-11x^2-186)\)
9. \(-7x^2+175=0\)
10. \(4(8x^2+7)=-(-27x^2-153)\)
11. \(4x^2-7=-2x^2-7\)
12. \(3x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+200=0 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(-2x^2-7=-7x^2-2 \\ \Leftrightarrow -2x^2+7x^2=-2+7 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(3(-7x^2+6)=-(24x^2-30) \\ \Leftrightarrow -21x^2+18=-24x^2+30 \\ \Leftrightarrow -21x^2+24x^2=30-18 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
4. \(-17x^2+1573=-9x^2+5 \\ \Leftrightarrow -17x^2+9x^2=5-1573 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(-5(-3x^2+2)=-(-22x^2+577) \\ \Leftrightarrow 15x^2-10=22x^2-577 \\ \Leftrightarrow 15x^2-22x^2=-577+10 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(3x^2-363=0 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(-11x^2-73=-7x^2-9 \\ \Leftrightarrow -11x^2+7x^2=-9+73 \\ \Leftrightarrow -4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5(-3x^2+2)=-(-11x^2-186) \\ \Leftrightarrow 15x^2-10=11x^2+186 \\ \Leftrightarrow 15x^2-11x^2=186+10 \\ \Leftrightarrow 4x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-7x^2+175=0 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(4(8x^2+7)=-(-27x^2-153) \\ \Leftrightarrow 32x^2+28=27x^2+153 \\ \Leftrightarrow 32x^2-27x^2=153-28 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
11. \(4x^2-7=-2x^2-7 \\ \Leftrightarrow 4x^2+2x^2=-7+7 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)