Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2+692=2x^2-8\)
2. \(8x^2-32=0\)
3. \(-4(4x^2+7)=-(15x^2+27)\)
4. \(2(10x^2+8)=-(-19x^2-80)\)
5. \(x^2-138=9x^2-10\)
6. \(3(-3x^2+2)=-(7x^2+156)\)
7. \(-5x^2-720=0\)
8. \(2x^2-98=0\)
9. \(-6x^2+150=0\)
10. \(5(-8x^2-5)=-(38x^2+25)\)
11. \(-4(-3x^2+4)=-(-4x^2-112)\)
12. \(-5(4x^2-2)=-(15x^2-1135)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2+692=2x^2-8 \\ \Leftrightarrow 9x^2-2x^2=-8-692 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(8x^2-32=0 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(-4(4x^2+7)=-(15x^2+27) \\ \Leftrightarrow -16x^2-28=-15x^2-27 \\ \Leftrightarrow -16x^2+15x^2=-27+28 \\ \Leftrightarrow -x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(10x^2+8)=-(-19x^2-80) \\ \Leftrightarrow 20x^2+16=19x^2+80 \\ \Leftrightarrow 20x^2-19x^2=80-16 \\ \Leftrightarrow x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(x^2-138=9x^2-10 \\ \Leftrightarrow x^2-9x^2=-10+138 \\ \Leftrightarrow -8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(-3x^2+2)=-(7x^2+156) \\ \Leftrightarrow -9x^2+6=-7x^2-156 \\ \Leftrightarrow -9x^2+7x^2=-156-6 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-5x^2-720=0 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(2x^2-98=0 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-6x^2+150=0 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(5(-8x^2-5)=-(38x^2+25) \\ \Leftrightarrow -40x^2-25=-38x^2-25 \\ \Leftrightarrow -40x^2+38x^2=-25+25 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-4(-3x^2+4)=-(-4x^2-112) \\ \Leftrightarrow 12x^2-16=4x^2+112 \\ \Leftrightarrow 12x^2-4x^2=112+16 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-5(4x^2-2)=-(15x^2-1135) \\ \Leftrightarrow -20x^2+10=-15x^2+1135 \\ \Leftrightarrow -20x^2+15x^2=1135-10 \\ \Leftrightarrow -5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{-5} < 0 \\ V = \varnothing \\ -----------------\)