Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+70=-3x^2+6\)
2. \(-7x^2-6=-8x^2-6\)
3. \(-7x^2+7=0\)
4. \(3(-8x^2-6)=-(23x^2+18)\)
5. \(-3x^2+300=0\)
6. \(4x^2-64=0\)
7. \(-13x^2+365=-10x^2+2\)
8. \(7x^2+0=0\)
9. \(-5x^2-80=0\)
10. \(-4x^2-316=-9x^2+4\)
11. \(-13x^2+41=-8x^2-4\)
12. \(-3(9x^2+5)=-(20x^2+862)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+70=-3x^2+6 \\ \Leftrightarrow -2x^2+3x^2=6-70 \\ \Leftrightarrow x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-7x^2-6=-8x^2-6 \\ \Leftrightarrow -7x^2+8x^2=-6+6 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-7x^2+7=0 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(3(-8x^2-6)=-(23x^2+18) \\ \Leftrightarrow -24x^2-18=-23x^2-18 \\ \Leftrightarrow -24x^2+23x^2=-18+18 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-3x^2+300=0 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(4x^2-64=0 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-13x^2+365=-10x^2+2 \\ \Leftrightarrow -13x^2+10x^2=2-365 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-5x^2-80=0 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4x^2-316=-9x^2+4 \\ \Leftrightarrow -4x^2+9x^2=4+316 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-13x^2+41=-8x^2-4 \\ \Leftrightarrow -13x^2+8x^2=-4-41 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-3(9x^2+5)=-(20x^2+862) \\ \Leftrightarrow -27x^2-15=-20x^2-862 \\ \Leftrightarrow -27x^2+20x^2=-862+15 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)