Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-4x^2-8)=-(-14x^2-42)\)
2. \(-3x^2+363=0\)
3. \(-4(5x^2-7)=-(24x^2-28)\)
4. \(12x^2-155=9x^2-8\)
5. \(-2(8x^2-4)=-(19x^2-596)\)
6. \(-7x^2-847=0\)
7. \(5(7x^2+4)=-(-37x^2+268)\)
8. \(-7x^2+1=-4x^2+4\)
9. \(-3x^2+27=0\)
10. \(6x^2-216=0\)
11. \(-2(10x^2-3)=-(24x^2-582)\)
12. \(12x^2+314=8x^2-10\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-4x^2-8)=-(-14x^2-42) \\ \Leftrightarrow 12x^2+24=14x^2+42 \\ \Leftrightarrow 12x^2-14x^2=42-24 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-3x^2+363=0 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(-4(5x^2-7)=-(24x^2-28) \\ \Leftrightarrow -20x^2+28=-24x^2+28 \\ \Leftrightarrow -20x^2+24x^2=28-28 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(12x^2-155=9x^2-8 \\ \Leftrightarrow 12x^2-9x^2=-8+155 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(-2(8x^2-4)=-(19x^2-596) \\ \Leftrightarrow -16x^2+8=-19x^2+596 \\ \Leftrightarrow -16x^2+19x^2=596-8 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-7x^2-847=0 \\ \Leftrightarrow -7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{-7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5(7x^2+4)=-(-37x^2+268) \\ \Leftrightarrow 35x^2+20=37x^2-268 \\ \Leftrightarrow 35x^2-37x^2=-268-20 \\ \Leftrightarrow -2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(-7x^2+1=-4x^2+4 \\ \Leftrightarrow -7x^2+4x^2=4-1 \\ \Leftrightarrow -3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3x^2+27=0 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(6x^2-216=0 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(-2(10x^2-3)=-(24x^2-582) \\ \Leftrightarrow -20x^2+6=-24x^2+582 \\ \Leftrightarrow -20x^2+24x^2=582-6 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(12x^2+314=8x^2-10 \\ \Leftrightarrow 12x^2-8x^2=-10-314 \\ \Leftrightarrow 4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{4} < 0 \\ V = \varnothing \\ -----------------\)