Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+100=0\)
2. \(5x^2+31=-2x^2+3\)
3. \(-2x^2+206=-6x^2+10\)
4. \(-8x^2-512=0\)
5. \(3x^2+0=0\)
6. \(5(8x^2+4)=-(-38x^2-182)\)
7. \(-5(10x^2+7)=-(53x^2+47)\)
8. \(10x^2+79=2x^2+7\)
9. \(3(5x^2+2)=-(-19x^2+30)\)
10. \(-8x^2+102=-10x^2+4\)
11. \(-4x^2-36=0\)
12. \(4(10x^2-3)=-(-36x^2-132)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+100=0 \\ \Leftrightarrow x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(5x^2+31=-2x^2+3 \\ \Leftrightarrow 5x^2+2x^2=3-31 \\ \Leftrightarrow 7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-2x^2+206=-6x^2+10 \\ \Leftrightarrow -2x^2+6x^2=10-206 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-8x^2-512=0 \\ \Leftrightarrow -8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{-8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(5(8x^2+4)=-(-38x^2-182) \\ \Leftrightarrow 40x^2+20=38x^2+182 \\ \Leftrightarrow 40x^2-38x^2=182-20 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-5(10x^2+7)=-(53x^2+47) \\ \Leftrightarrow -50x^2-35=-53x^2-47 \\ \Leftrightarrow -50x^2+53x^2=-47+35 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(10x^2+79=2x^2+7 \\ \Leftrightarrow 10x^2-2x^2=7-79 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(5x^2+2)=-(-19x^2+30) \\ \Leftrightarrow 15x^2+6=19x^2-30 \\ \Leftrightarrow 15x^2-19x^2=-30-6 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(-8x^2+102=-10x^2+4 \\ \Leftrightarrow -8x^2+10x^2=4-102 \\ \Leftrightarrow 2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4x^2-36=0 \\ \Leftrightarrow -4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4(10x^2-3)=-(-36x^2-132) \\ \Leftrightarrow 40x^2-12=36x^2+132 \\ \Leftrightarrow 40x^2-36x^2=132+12 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)