Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+7=2x^2+7\)
2. \(2x^2-50=0\)
3. \(4(10x^2-2)=-(-41x^2+204)\)
4. \(-9x^2-777=-5x^2+7\)
5. \(5x^2+125=0\)
6. \(9x^2-98=6x^2+10\)
7. \(-4x^2+256=0\)
8. \(-3x^2-371=-6x^2-8\)
9. \(2x^2-285=-4x^2+9\)
10. \(-8x^2+72=0\)
11. \(18x^2-10=10x^2-10\)
12. \(x^2+70=8x^2+7\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+7=2x^2+7 \\ \Leftrightarrow -6x^2-2x^2=7-7 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(2x^2-50=0 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(4(10x^2-2)=-(-41x^2+204) \\ \Leftrightarrow 40x^2-8=41x^2-204 \\ \Leftrightarrow 40x^2-41x^2=-204+8 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(-9x^2-777=-5x^2+7 \\ \Leftrightarrow -9x^2+5x^2=7+777 \\ \Leftrightarrow -4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(5x^2+125=0 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(9x^2-98=6x^2+10 \\ \Leftrightarrow 9x^2-6x^2=10+98 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(-4x^2+256=0 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-3x^2-371=-6x^2-8 \\ \Leftrightarrow -3x^2+6x^2=-8+371 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(2x^2-285=-4x^2+9 \\ \Leftrightarrow 2x^2+4x^2=9+285 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(-8x^2+72=0 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(18x^2-10=10x^2-10 \\ \Leftrightarrow 18x^2-10x^2=-10+10 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(x^2+70=8x^2+7 \\ \Leftrightarrow x^2-8x^2=7-70 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)