Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+900=0\)
2. \(4x^2+19=-2x^2-5\)
3. \(-7x^2-700=0\)
4. \(-4x^2+484=0\)
5. \(-4(-6x^2-3)=-(-25x^2-181)\)
6. \(-5x^2-42=-4x^2-6\)
7. \(3x^2-182=10x^2-7\)
8. \(-8x^2+0=0\)
9. \(-3x^2+810=5x^2+10\)
10. \(-5x^2+845=0\)
11. \(7x^2+77=9x^2+5\)
12. \(2x^2-2=5x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+900=0 \\ \Leftrightarrow 4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(4x^2+19=-2x^2-5 \\ \Leftrightarrow 4x^2+2x^2=-5-19 \\ \Leftrightarrow 6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-7x^2-700=0 \\ \Leftrightarrow -7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{-7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-4x^2+484=0 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(-4(-6x^2-3)=-(-25x^2-181) \\ \Leftrightarrow 24x^2+12=25x^2+181 \\ \Leftrightarrow 24x^2-25x^2=181-12 \\ \Leftrightarrow -x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{-1} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5x^2-42=-4x^2-6 \\ \Leftrightarrow -5x^2+4x^2=-6+42 \\ \Leftrightarrow -x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(3x^2-182=10x^2-7 \\ \Leftrightarrow 3x^2-10x^2=-7+182 \\ \Leftrightarrow -7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{-7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-3x^2+810=5x^2+10 \\ \Leftrightarrow -3x^2-5x^2=10-810 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(-5x^2+845=0 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(7x^2+77=9x^2+5 \\ \Leftrightarrow 7x^2-9x^2=5-77 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(2x^2-2=5x^2-5 \\ \Leftrightarrow 2x^2-5x^2=-5+2 \\ \Leftrightarrow -3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{-3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)