Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2-1176=0\)
2. \(-4(-10x^2-9)=-(-36x^2-100)\)
3. \(-3x^2-1014=-10x^2-6\)
4. \(x^2+0=0\)
5. \(7x^2+448=0\)
6. \(-8x^2-1568=0\)
7. \(3x^2+90=4x^2-10\)
8. \(-5(6x^2-7)=-(34x^2+221)\)
9. \(2x^2-338=0\)
10. \(-3(-5x^2+6)=-(-8x^2-829)\)
11. \(2x^2-6=8x^2-6\)
12. \(6x^2-579=2x^2-3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2-1176=0 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-4(-10x^2-9)=-(-36x^2-100) \\ \Leftrightarrow 40x^2+36=36x^2+100 \\ \Leftrightarrow 40x^2-36x^2=100-36 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(-3x^2-1014=-10x^2-6 \\ \Leftrightarrow -3x^2+10x^2=-6+1014 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(x^2+0=0 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(7x^2+448=0 \\ \Leftrightarrow 7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-8x^2-1568=0 \\ \Leftrightarrow -8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{-8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(3x^2+90=4x^2-10 \\ \Leftrightarrow 3x^2-4x^2=-10-90 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-5(6x^2-7)=-(34x^2+221) \\ \Leftrightarrow -30x^2+35=-34x^2-221 \\ \Leftrightarrow -30x^2+34x^2=-221-35 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2x^2-338=0 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-3(-5x^2+6)=-(-8x^2-829) \\ \Leftrightarrow 15x^2-18=8x^2+829 \\ \Leftrightarrow 15x^2-8x^2=829+18 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(2x^2-6=8x^2-6 \\ \Leftrightarrow 2x^2-8x^2=-6+6 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(6x^2-579=2x^2-3 \\ \Leftrightarrow 6x^2-2x^2=-3+579 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)