Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+340=2x^2-3\)
2. \(4(7x^2-9)=-(-33x^2-569)\)
3. \(-3x^2-48=0\)
4. \(8x^2+648=0\)
5. \(-3x^2-1000=4x^2+8\)
6. \(5(9x^2-7)=-(-41x^2+31)\)
7. \(-4(5x^2+8)=-(18x^2+30)\)
8. \(2(9x^2+8)=-(-16x^2-408)\)
9. \(-5x^2+0=0\)
10. \(17x^2+797=9x^2-3\)
11. \(-3(-10x^2+4)=-(-36x^2-282)\)
12. \(-7x^2+700=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+340=2x^2-3 \\ \Leftrightarrow -5x^2-2x^2=-3-340 \\ \Leftrightarrow -7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{-7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(4(7x^2-9)=-(-33x^2-569) \\ \Leftrightarrow 28x^2-36=33x^2+569 \\ \Leftrightarrow 28x^2-33x^2=569+36 \\ \Leftrightarrow -5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{-5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-3x^2-48=0 \\ \Leftrightarrow -3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(8x^2+648=0 \\ \Leftrightarrow 8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3x^2-1000=4x^2+8 \\ \Leftrightarrow -3x^2-4x^2=8+1000 \\ \Leftrightarrow -7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{-7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(5(9x^2-7)=-(-41x^2+31) \\ \Leftrightarrow 45x^2-35=41x^2-31 \\ \Leftrightarrow 45x^2-41x^2=-31+35 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-4(5x^2+8)=-(18x^2+30) \\ \Leftrightarrow -20x^2-32=-18x^2-30 \\ \Leftrightarrow -20x^2+18x^2=-30+32 \\ \Leftrightarrow -2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(2(9x^2+8)=-(-16x^2-408) \\ \Leftrightarrow 18x^2+16=16x^2+408 \\ \Leftrightarrow 18x^2-16x^2=408-16 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(17x^2+797=9x^2-3 \\ \Leftrightarrow 17x^2-9x^2=-3-797 \\ \Leftrightarrow 8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3(-10x^2+4)=-(-36x^2-282) \\ \Leftrightarrow 30x^2-12=36x^2+282 \\ \Leftrightarrow 30x^2-36x^2=282+12 \\ \Leftrightarrow -6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{-6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-7x^2+700=0 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)