Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2-57=2x^2-3\)
2. \(5(-4x^2-3)=-(13x^2+22)\)
3. \(7x^2+2=4x^2-10\)
4. \(3(9x^2+6)=-(-22x^2-23)\)
5. \(-5(4x^2+9)=-(17x^2+408)\)
6. \(6x^2-600=0\)
7. \(14x^2+11=8x^2+5\)
8. \(-13x^2-18=-10x^2+9\)
9. \(-5(-9x^2-6)=-(-42x^2+645)\)
10. \(-4(9x^2+8)=-(31x^2+32)\)
11. \(x^2-1=0\)
12. \(2x^2-2=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2-57=2x^2-3 \\ \Leftrightarrow 8x^2-2x^2=-3+57 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(5(-4x^2-3)=-(13x^2+22) \\ \Leftrightarrow -20x^2-15=-13x^2-22 \\ \Leftrightarrow -20x^2+13x^2=-22+15 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(7x^2+2=4x^2-10 \\ \Leftrightarrow 7x^2-4x^2=-10-2 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3(9x^2+6)=-(-22x^2-23) \\ \Leftrightarrow 27x^2+18=22x^2+23 \\ \Leftrightarrow 27x^2-22x^2=23-18 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-5(4x^2+9)=-(17x^2+408) \\ \Leftrightarrow -20x^2-45=-17x^2-408 \\ \Leftrightarrow -20x^2+17x^2=-408+45 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(6x^2-600=0 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(14x^2+11=8x^2+5 \\ \Leftrightarrow 14x^2-8x^2=5-11 \\ \Leftrightarrow 6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-13x^2-18=-10x^2+9 \\ \Leftrightarrow -13x^2+10x^2=9+18 \\ \Leftrightarrow -3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-5(-9x^2-6)=-(-42x^2+645) \\ \Leftrightarrow 45x^2+30=42x^2-645 \\ \Leftrightarrow 45x^2-42x^2=-645-30 \\ \Leftrightarrow 3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4(9x^2+8)=-(31x^2+32) \\ \Leftrightarrow -36x^2-32=-31x^2-32 \\ \Leftrightarrow -36x^2+31x^2=-32+32 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(x^2-1=0 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(2x^2-2=0 \\ \Leftrightarrow 2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)