Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-2x^2-8)=-(16x^2+424)\)
2. \(2(-7x^2-2)=-(20x^2-20)\)
3. \(8x^2-968=0\)
4. \(x^2-169=0\)
5. \(-2x^2+392=0\)
6. \(-x^2+239=-6x^2-6\)
7. \(-2(3x^2-4)=-(14x^2+64)\)
8. \(4(-3x^2-6)=-(7x^2+869)\)
9. \(-4(-6x^2+2)=-(-28x^2+4)\)
10. \(-8x^2+968=0\)
11. \(-4x^2+0=0\)
12. \(5x^2+516=-3x^2+4\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-2x^2-8)=-(16x^2+424) \\ \Leftrightarrow -10x^2-40=-16x^2-424 \\ \Leftrightarrow -10x^2+16x^2=-424+40 \\ \Leftrightarrow 6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(2(-7x^2-2)=-(20x^2-20) \\ \Leftrightarrow -14x^2-4=-20x^2+20 \\ \Leftrightarrow -14x^2+20x^2=20+4 \\ \Leftrightarrow 6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(8x^2-968=0 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(x^2-169=0 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(-2x^2+392=0 \\ \Leftrightarrow -2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-x^2+239=-6x^2-6 \\ \Leftrightarrow -x^2+6x^2=-6-239 \\ \Leftrightarrow 5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2(3x^2-4)=-(14x^2+64) \\ \Leftrightarrow -6x^2+8=-14x^2-64 \\ \Leftrightarrow -6x^2+14x^2=-64-8 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(4(-3x^2-6)=-(7x^2+869) \\ \Leftrightarrow -12x^2-24=-7x^2-869 \\ \Leftrightarrow -12x^2+7x^2=-869+24 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-4(-6x^2+2)=-(-28x^2+4) \\ \Leftrightarrow 24x^2-8=28x^2-4 \\ \Leftrightarrow 24x^2-28x^2=-4+8 \\ \Leftrightarrow -4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-8x^2+968=0 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5x^2+516=-3x^2+4 \\ \Leftrightarrow 5x^2+3x^2=4-516 \\ \Leftrightarrow 8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{8} < 0 \\ V = \varnothing \\ -----------------\)