Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+703=-2x^2+3\)
2. \(3(-10x^2+6)=-(34x^2-418)\)
3. \(-3(-3x^2+3)=-(-x^2-959)\)
4. \(4(10x^2-8)=-(-37x^2-16)\)
5. \(-5x^2+5=0\)
6. \(-3x^2+692=4x^2-8\)
7. \(-2(-10x^2-4)=-(-27x^2+1000)\)
8. \(9x^2+93=10x^2-7\)
9. \(-6x^2+0=0\)
10. \(-10x^2+515=-7x^2+8\)
11. \(2(10x^2+9)=-(-14x^2-618)\)
12. \(x^2+49=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+703=-2x^2+3 \\ \Leftrightarrow 5x^2+2x^2=3-703 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3(-10x^2+6)=-(34x^2-418) \\ \Leftrightarrow -30x^2+18=-34x^2+418 \\ \Leftrightarrow -30x^2+34x^2=418-18 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-3(-3x^2+3)=-(-x^2-959) \\ \Leftrightarrow 9x^2-9=x^2+959 \\ \Leftrightarrow 9x^2-x^2=959+9 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(4(10x^2-8)=-(-37x^2-16) \\ \Leftrightarrow 40x^2-32=37x^2+16 \\ \Leftrightarrow 40x^2-37x^2=16+32 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(-5x^2+5=0 \\ \Leftrightarrow -5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{-5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-3x^2+692=4x^2-8 \\ \Leftrightarrow -3x^2-4x^2=-8-692 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(-2(-10x^2-4)=-(-27x^2+1000) \\ \Leftrightarrow 20x^2+8=27x^2-1000 \\ \Leftrightarrow 20x^2-27x^2=-1000-8 \\ \Leftrightarrow -7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{-7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(9x^2+93=10x^2-7 \\ \Leftrightarrow 9x^2-10x^2=-7-93 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-10x^2+515=-7x^2+8 \\ \Leftrightarrow -10x^2+7x^2=8-515 \\ \Leftrightarrow -3x^2 = -507 \\ \Leftrightarrow x^2 = \frac{-507}{-3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(2(10x^2+9)=-(-14x^2-618) \\ \Leftrightarrow 20x^2+18=14x^2+618 \\ \Leftrightarrow 20x^2-14x^2=618-18 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(x^2+49=0 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)