Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(4x^2+9)=-(4x^2-45)\)
2. \(-6x^2+508=2x^2-4\)
3. \(-5(10x^2+10)=-(43x^2+897)\)
4. \(-x^2+25=0\)
5. \(-4x^2-11=-5x^2-7\)
6. \(4(4x^2-8)=-(-11x^2+157)\)
7. \(x^2-49=0\)
8. \(x^2-169=0\)
9. \(-4(-9x^2-3)=-(-43x^2+51)\)
10. \(7x^2+0=0\)
11. \(4x^2-13=-4x^2-5\)
12. \(3(4x^2-9)=-(-10x^2-23)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(4x^2+9)=-(4x^2-45) \\ \Leftrightarrow -12x^2-27=-4x^2+45 \\ \Leftrightarrow -12x^2+4x^2=45+27 \\ \Leftrightarrow -8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-6x^2+508=2x^2-4 \\ \Leftrightarrow -6x^2-2x^2=-4-508 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(-5(10x^2+10)=-(43x^2+897) \\ \Leftrightarrow -50x^2-50=-43x^2-897 \\ \Leftrightarrow -50x^2+43x^2=-897+50 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(-x^2+25=0 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-4x^2-11=-5x^2-7 \\ \Leftrightarrow -4x^2+5x^2=-7+11 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(4(4x^2-8)=-(-11x^2+157) \\ \Leftrightarrow 16x^2-32=11x^2-157 \\ \Leftrightarrow 16x^2-11x^2=-157+32 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(x^2-169=0 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-4(-9x^2-3)=-(-43x^2+51) \\ \Leftrightarrow 36x^2+12=43x^2-51 \\ \Leftrightarrow 36x^2-43x^2=-51-12 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(4x^2-13=-4x^2-5 \\ \Leftrightarrow 4x^2+4x^2=-5+13 \\ \Leftrightarrow 8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(3(4x^2-9)=-(-10x^2-23) \\ \Leftrightarrow 12x^2-27=10x^2+23 \\ \Leftrightarrow 12x^2-10x^2=23+27 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)