Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-2x^2-4)=-(-7x^2-5)\)
2. \(-4x^2+900=0\)
3. \(11x^2+4=4x^2+4\)
4. \(-16x^2+457=-9x^2+9\)
5. \(8x^2+648=0\)
6. \(7x^2-259=3x^2-3\)
7. \(x^2-1345=9x^2+7\)
8. \(-3x^2+145=-6x^2-2\)
9. \(-2(-6x^2+9)=-(-10x^2-320)\)
10. \(6x^2+190=9x^2-2\)
11. \(-5x^2+850=2x^2+3\)
12. \(x^2+21=8x^2-7\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-2x^2-4)=-(-7x^2-5) \\ \Leftrightarrow 4x^2+8=7x^2+5 \\ \Leftrightarrow 4x^2-7x^2=5-8 \\ \Leftrightarrow -3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{-3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(-4x^2+900=0 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(11x^2+4=4x^2+4 \\ \Leftrightarrow 11x^2-4x^2=4-4 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-16x^2+457=-9x^2+9 \\ \Leftrightarrow -16x^2+9x^2=9-457 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(8x^2+648=0 \\ \Leftrightarrow 8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(7x^2-259=3x^2-3 \\ \Leftrightarrow 7x^2-3x^2=-3+259 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(x^2-1345=9x^2+7 \\ \Leftrightarrow x^2-9x^2=7+1345 \\ \Leftrightarrow -8x^2 = 1352 \\ \Leftrightarrow x^2 = \frac{1352}{-8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3x^2+145=-6x^2-2 \\ \Leftrightarrow -3x^2+6x^2=-2-145 \\ \Leftrightarrow 3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-2(-6x^2+9)=-(-10x^2-320) \\ \Leftrightarrow 12x^2-18=10x^2+320 \\ \Leftrightarrow 12x^2-10x^2=320+18 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(6x^2+190=9x^2-2 \\ \Leftrightarrow 6x^2-9x^2=-2-190 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-5x^2+850=2x^2+3 \\ \Leftrightarrow -5x^2-2x^2=3-850 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(x^2+21=8x^2-7 \\ \Leftrightarrow x^2-8x^2=-7-21 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)